Worksheets for GCSE Mathematics. Probability. mrmathematics.com Maths Resources for Teachers. Handling Data


 Kellie Fox
 1 years ago
 Views:
Transcription
1 Worksheets for GCSE Mathematics Probability mrmathematics.com Maths Resources for Teachers Handling Data
2 Probability Worksheets Contents Differentiated Independent Learning Worksheets Probability Scales Page 30 Writing Probabilities Page 30 Expected Frequencies Page 50 Sample Space Diagrams Page 60 Mutually Exclusive Events Page 70 Probability Trees Page 80 Venn Diagrams Page 90 Conditional Events Page 10 Union and Intersection of Sets Page 11 Solutions Probability Scales Writing Probabilities Expected Frequencies Sample Space Diagrams Mutually Exclusive Events Probability Trees Venn Diagrams Conditional Events Page 12 Page 13 Page 14 Page 15 Page 16 Page 17 Page 18 Page 19 Union and Intersection of Sets Page 20
3 Probability Scale Q1. Use these keywords to describe the likelihood of the following events. It will be Tuesday the day after Thursday. b) A fair coin will land on heads. c) The sun will come up today. d) It will rain tomorrow. e) You will arrive on time to school tomorrow. f) You will celebrate your 60 th birthday tomorrow. g) The next car you see will be a Ferrari. Q2. LE Suzie reaches into the box to pick a ball at random. Place these events along the probability scale to describe their likelihood. Picking a green ball. b) Picking a coloured ball. c) Picking a red ball. d) Picking a red or black ball. e) Picking an orange coloured ball. Q3. Write in six different events that can be placed as shown along the probability scale below. 3
4 Writing Probabilities Q1. A ball is taken at random from this box. Write the following probabilities; leave your answer as a simplified fraction. P (Red) b) P (Blue) c) P (Purple) d) P (Red or purple) e) P (Black) f) P (Not Black) Q2. The arrow is spun around the spinner so it lands randomly on a number. Write the following probabilities; leave your answer as a simplified fraction. P (5 or 6) b) P (Odd number) LE c) P (Less than 6) d) P (Greater than 7) e) P (Factor of 12) f) P (Multiple of 3) Q3. Here are two spinners. Which spinner has P (White) =? b) Which spinner has P (Blue) =? c) Which spinner has P (1) =? d) Which spinner has P (2) =? Q4. An ordinary six sided dice is rolled. Work out the probability of getting a 4 b) an even number c) a 8 d) a number greater than 2 e) a number less than 7 f) zero. Q5. A bag contains red and blue counters only. The probability of pick a red is. What is the probability of picking a blue? 4
5 Q1. A fair six sided dice is thrown. What is the probability of the throwing a Expected Frequency i) Three ii) One iii) Prime Number iv) Less than six b) Land on a 4 number after 300 throws? c) Land on an even number after 120 throws? d) Land on a prime number after 120 throws? e) Land on a number less than six after 240 throws? Q2. A spinner, with 12 equal sections, is spun 240 times. How often would you expect to spin: a shaded section b) an even number c) number 3 d) square number e) a prime number and shaded section LE Q3. This pentagonal spinner is spun 100 times with the results recorded. Here are the results. What is the probability of the spinner landing on the colour i) Red ii) Green iii) Blue iv) White? b) How many times would you expect the spinner to land on each colour after 500 spins? c) How many times would you expect the spinner to land on each colour after 1000 spins? Q4 A coin is biased so that the probability of tossing a head is 0.7. How many heads would you expect when the coin is tossed 100 times? b) How many tails would you expect when the coin is tossed 300 times? Q5. Players, at a village fayre, pay 1 to spin the pointed on the board shown. Players win the amount shown by the pointer. The game is played 600 times. Work out the expected profit or loss on the game. 5
6 Q1. Sample Space Diagrams 20p and 50p coins are tossed at the same time. List all the possible outcomes. b) Calculate the probability of tossing two heads. c) Calculate the probability of tossing a head or tails in any order. Q2. The spinner shown has three equal sections on the inside and six on the outside. List all the possible outcomes. b) Calculate the probability of spinning a i) number 2 ii) C iii) 3 and B iv) 5 and A v) C and 6 vi) Not B and 3 LE Q3. A fair coin is tossed and a fair dice is rolled. Q4. Complete the sample space diagram to show all the possible outcomes. What is the probability of obtaining: a head and six b) a tail and odd number c) a head and greater than 2 d) a tail and less than 3 e) a prime number f) a head and 5 or tail and 1 The diagram shows a fair spinner dividing into three equal sections. The spinner is spun twice and the numbers are added together. Complete a sample space diagram to show all the possible scores. b) Calculate the probability of getting a score of: i) 2 ii) 5 iii) square number iv) odd number v) Less than 10 vi) Greater than 6 Q5. The diagram shows two sets of card Hearts and Clubs. One card is taken at random from each set. List all the possible outcomes. b) What is the probability of 6 i) Ace and 8 ii) Hearts and 7 iii) Clubs and 2 iv) Hearts and Clubs
7 Mutually Exclusive Events Q1. The scale shows the probability that a fair six sided dice will land on the number 5. Calculate the probability of the dice not landing on a five. Q2. The probability that Adam wins a raffle is 15%. Calculate the probability that Adam does win the raffle. Q3. A bad contains red, black and blue balls. The probability of picking a red ball is 0.4. The probability of picking a black ball is Calculate the probability of picking a black ball. Q4. A bag contains blue, red, green orange and black marbles. The table shows the probabilities of picking each marble at random. LE How can you tell there is a mistake in the table? b) The probability of picking a red marble is wrong. What should it be? c) What is the probability of picking a marble that is black, orange or red? d) What is the probability of picking a marble that is not blue? Q5. A spinner is shown with the probabilities of landing on each colour recorded. What is the probability of the spinner landing on one of the following? Not Pink b) Pink c) Not Green d) Not Red Q6. A bag contains only red, blue, green, black and purple counters. The probabilities for picking blue, black and purple counters are recorded. The probabilities of picking a green and red counter are equal. Calculate the probability of picking a red and green counter. b) The spinner is spun 300 times. How many reds would you expect to record? 7
8 Q1. b) c) d) Q2. b) c) d) e) Q3. b) c) d) Probability Trees A bag contains only red and blue counters. There are 4 red and 1 blue. Paul takes a counter from the bag at random and replaces it. Complete the tree diagram to show the possible outcomes. Calculate the probability of: taking out two red counters. taking out two different colours. not taking a red counter. The train network has stated that 85% of trains arrive on time. Gemma has to take two trains on her way to work. Complete the tree diagram. LE What is the probability that: the first train is on time but the second one is late. at least one train is late. both trains are late. neither train is late. Along Joanna s drive to work she crosses two traffic lights that are independent of each other. The probability she is stuck at the first light is 0.6. The probability of being stopped at the second light is 0.5. Calculate the probability that on a given day: she stops at both sets of lights. Joanna stops at the first set but not the other. Joanna does not have to stop. she stops for at least one set. Q4. A couple has three children. It is equally likely that each child is a boy or girl. Draw a probability tree to show the possible genders of each baby. Use the probability tree to calculate: all three are girls b) they have one boy and two girls 8 c) they have at least two boys. d) they have no girls. e) they have at least one girl. e) they have at least one boy and one girl.
9 Q1. Venn Diagrams The Venn diagrams show the subjects taken by a group of 60 college students. Work out the value of x in each case. b) c) Q2. In form 10J 15 students are studying Maths, 12 students are studying French, 6 are studying both and 3 students study neither. Complete a Venn Diagram to represent this data. b) How many students are there in the form? A student is chosen at random. c) Calculate the probability that the students chooses Maths or French but not both. LE Q3. Of the households in the United Kingdom 35% have a L.E.D. TV and 60% have a Bluray player. There are 24% that have both. Complete a Venn Diagram to show this information. b) Calculate the probability that a household chosen at random has either a L.E.D. TV or a Bluray player but not both. c) Calculate the probability that a household chosen at random has neither a L.E.D. TV nor a Bluray player. Q4. A survey of 100 people at a local gym were asked how they spend their time there. 34 people used the free weights. 28 people used cardiovascular equipment 38 people went to the classes. There were 9 who used the weights and went to classes, 5 who used the cardiovascular equipment and went to classes and 10 who used the free weights and cardiovascular equipment. 4 people made use of all three facilities. Represent these data on a Venn diagram. A person was selected at random from this group. Find the probability that this person b) i) used the free weights but did not use the cardiovascular equipment. ii) went to the classes but did not use free weights. ii) only used two of the three facilities. 9
10 Conditional Probability Q1. A bag contains three white balls and two black. A ball is taken out at random and not replaced. Another is then taken out. Draw a tree diagram to calculate the probability that: both balls will be white. b) one ball of each colour is removed. Q2. Of the 15 M&Ms left in a bag, 8 are red and the rest are blue. Dominic chooses two of these random, one after the other. Draw a tree diagram to calculate the probability that Dominic chooses: both red. b) one of each colour. c) both the same colour d) at least one blue. Q3. On Kelly s way to work she passes two sets of traffic lights. The probability that the first is green is. If the first is green, the probability that the second is green is. If the first is red the probability that the second is green is. LE What is the probability that: both are red b) none are red c) only one is green d) at least one is green. Q4. The probability of passing a test at the first attempt is Those who fail are allowed a resit. The probability of passing the resit is 0.8. What is the probability of failing at the second attempt? Q5. 65% of people over the age of 60 have the flu vaccination. Of those who do not have the vaccination 75% get the flu. Calculate the probability that a person over the age of 60 will get the flu. Q6. Pauline has twenty biscuits in a tin. 6 are ginger, 12 are plain and the rest are chocolate. Pauline takes two biscuits out of the tin. Draw a tree diagram to work out the probability the two were not the same type. Q7. There are three different types of sandwiches in a shop. There are 5 salads, 4 cheese and 2 ham. Jodie takes two sandwiches at random. Calculate the probability that she takes two sandwiches of the same type. Q8. There are 8 coins in a box. Five and 1 coins and three are 20p coins. George takes 3 coins at random from the box. Work out the probability that he takes exactly
11 Q1 Use set notation to describe the shaded area in each Venn diagram. b) c) d) Q2 For the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}: Q3 A = {multiples of 2} AA BB = {4} AA BB = {1, 2,4, 6, 8, 9, 10) Draw a Venn diagram for this information. A card is selected at random from a pack of 52 playing cards. Let K be the event that the card is a king and D the event that the card is a diamond. Complete the Venn diagram. b) Find each of these: i) PP(KK DD) ii) PP(KK DD) iii) PP(KK ) iv) PP(KK DD) Q4 X and Y are two events and P(X) = 0.6, P(Y) = 0.7 and P(X Y) = 0.9. Find i) PP(XX YY) ii) PP(XX ) iii) PP(XX YY) iv) PP(XX YY) 11 Union and Intersection Set Notation LE
12 Probability Scale Q1. Impossible b) Evens c) Certain d) Likely/Unlikely depending on the time of year. e) Likely f) Impossible g) Unlikely Q2. 12 Solutions LE
13 Writing Probabilities Q1. P (Red) = d) P (Red or purple) = Q2.. P (5 or 6) = d) P (Greater than 7) = Q3. b) P (Blue) = c) P (Purple) = e) P (Black) =0 f) P (Not Black) =1 b) P (Odd number) = e) P (Factor of 12) = Spinner B b) Spinner A c) Spinner A d) Spinner B Q4. LE P(4) = d) P(>2) = Q5. P (Blue) = 13 c) P (Less than 6) = f) P (Multiple of 3) = b) P(Even) = c) P(8) =0 e) P(<7) =1 f) P(0) =0
14 Expected Frequency Q1. i) P (3) = b) Landing on 4 = 50 times c) Landing on even = 60 times ii) P (1) = d) Landing on prime = 60 times e) Landing on 6 = 40 times Q2. Shaded section = 120 times b) Even number = 120 times c) Number 3 = 40 times d) Square number = 120 times e) Prime and Shaded= 40 times Q3. iii) P (Prime) = LE Red = b) Green = c) Blue = iv) P (<6) = d) White = 0 b) Red = 100 times Green = 125 times Blue = 275 times c) Red = 200 times Green = 250 times Blue = 550 times Q4 70 times b) 90 times Q5. Profit of
15 Sample Space Diagrams Q1. HH, HT, TH, TT b) P (HH) = Q2. A1, A2, B3, B4, C5, C6, b) i) P (Number 2) = Q3. iii) P(3 and B) = v) P (C and 6) = H1, H2, H3, H4, H5, H6 T1, T2, T3, T4, T5, T6 d) ii) P (C) = iv) P (5 and A) = 0 vi) P (Not B or 3) = b) LE Q4. b) Q5. i) iv) 0 b) i) iii) 15 e) ii) ii) 0 v) iv) 1 c) P (HT or TH) = c) f) iii) vi)
16 Mutually Exclusive Events Q1. P (not 5) = Q2. P (Losing Raffle) = 85% Q3. P (Black ball) = 0.45 Q4. Sum of probabilities not equal to 100%. b) P (red) = 15% c) P (Black or Orange or Red) = 50% d) P (Not Blue) = 70% Q5. P (Not Pink) = 0.98 b) P (Pink) = 0.02 c) P (Not Green) = 0.85 d) P (Not Red) = 0.72 Q6. LE P (Red) = P (Green) = 0.12 b) 36 Reds. 16
17 Probability Trees Q1. A) b) P (R&R) = Q2. c) P (R&B or B&R) = d) P (not R) = b) P (On time & Late) = 12.75% c) P (at least one late) = 27.75% d) P (Late& Late) = 2.25% e) P ( neither late) = 72.25% Q3. P (S& S) = 0.36 b) P (S& G) = 0.24 c) P (not S) = 0.16 d) P ( S at least once) = 0.16 Q4. LE P (all three are girls) = c) P (at least two boys) = e) P (at least one girl) = 17 b) P (one boy and two girls)= d) P (no girls) = e) P (at least one boy and one girl) =
18 Solutions Q1. x = 8 b) x = 10 c) x = 7 Q2. b) 24 c) Q3. b) 24 % c) 29% Q4. b) i) ii) iii) Venn Diagrams LE
19 Solutions Q1. Q2. Q3. P (both are red) =!! c) P (only one is green) =!! Q4. P (Failure at second attempt) = 7% Conditional Probability P (both balls will be white) =! b) P (one ball of each colour is removed) =!! P (both red) =!!" b) P (one of each colour) =!!" c) P (both the same colour) =!" d) P (at least one blue) =!! Q5. P (person over the age of 60 will get the flu) = 26.25% Q6. LE Q7. P (two sandwiches of the same type) =!" Q8. P ( 2.20) =!"!" 19 P (not the same type) =!"!!!"!"!" b) P (none are red) =!! d) P (at least one is green) =!!!"
20 Q1 PP(AA BB) b) PP(AA BB) c) PP (AA BB) d) PP (AA BB) Q2 Q3 20 b) i) PP(KK DD) = 1 52 Q4 Union and Intersection Set Notation LE ii) PP(KK DD) = 4 13 iii) PP(KK ) = 12 i) PP(XX YY) = 0.4 ii) PP(XX ) = 0.4 iii) PP(XX YY) = 0.8 iv) PP(XX YY) = iv) PP(KK DD) = 3 13
MEP Practice Book SA5
5 Probability 5.1 Probabilities MEP Practice Book SA5 1. Describe the probability of the following events happening, using the terms Certain Very likely Possible Very unlikely Impossible (d) (e) (f) (g)
More informationMEP Practice Book ES5. 1. A coin is tossed, and a die is thrown. List all the possible outcomes.
5 Probability MEP Practice Book ES5 5. Outcome of Two Events 1. A coin is tossed, and a die is thrown. List all the possible outcomes. 2. A die is thrown twice. Copy the diagram below which shows all the
More informationPROBABILITY. 1. Introduction. Candidates should able to:
PROBABILITY Candidates should able to: evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g for the total score when two fair dice are thrown), or by calculation
More informationProbability 1. Name: Total Marks: 1. An unbiased spinner is shown below.
Probability 1 A collection of 91 Maths GCSE Sample and Specimen questions from AQA, OCR and PearsonEdexcel. Name: Total Marks: 1. An unbiased spinner is shown below. (a) Write a number to make each sentence
More informationSection A Calculating Probabilities & Listing Outcomes Grade F D
Name: Teacher Assessment Section A Calculating Probabilities & Listing Outcomes Grade F D 1. A fair ordinary sixsided dice is thrown once. The boxes show some of the possible outcomes. Draw a line from
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Study Guide for Test III (MATH 1630) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the number of subsets of the set. 1) {x x is an even
More informationTopic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes
Worksheet 6 th Topic : ADDITION OF PROBABILITIES (MUTUALLY EXCLUSIVE EVENTS) TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of
More informationLC OL Probability. ARNMaths.weebly.com. As part of Leaving Certificate Ordinary Level Math you should be able to complete the following.
A Ryan LC OL Probability ARNMaths.weebly.com Learning Outcomes As part of Leaving Certificate Ordinary Level Math you should be able to complete the following. Counting List outcomes of an experiment Apply
More informationPROBABILITY M.K. HOME TUITION. Mathematics Revision Guides. Level: GCSE Foundation Tier
Mathematics Revision Guides Probability Page 1 of 18 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier PROBABILITY Version: 2.1 Date: 08102015 Mathematics Revision Guides Probability
More informationA. 15 B. 24 C. 45 D. 54
A spinner is divided into 8 equal sections. Lara spins the spinner 120 times. It lands on purple 30 times. How many more times does Lara need to spin the spinner and have it land on purple for the relative
More informationThis unit will help you work out probability and use experimental probability and frequency trees. Key points
Get started Probability This unit will help you work out probability and use experimental probability and frequency trees. AO Fluency check There are 0 marbles in a bag. 9 of the marbles are red, 7 are
More informationProbability Essential Math 12 Mr. Morin
Probability Essential Math 12 Mr. Morin Name: Slot: Introduction Probability and Odds Single Event Probability and Odds Two and Multiple Event Experimental and Theoretical Probability Expected Value (Expected
More informationProbability. Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible
Probability Sometimes we know that an event cannot happen, for example, we cannot fly to the sun. We say the event is impossible Impossible In summer, it doesn t rain much in Cape Town, so on a chosen
More informationSTRAND: PROBABILITY Unit 2 Probability of Two or More Events
STRAND: PROAILITY Unit 2 Probability of Two or More Events TEXT Contents Section 2. Outcome of Two Events 2.2 Probability of Two Events 2. Use of Tree Diagrams 2 Probability of Two or More Events 2. Outcome
More informationPage 1 of 22. Website: Mobile:
Exercise 15.1 Question 1: Complete the following statements: (i) Probability of an event E + Probability of the event not E =. (ii) The probability of an event that cannot happen is. Such as event is called.
More informationModule 4 Project Maths Development Team Draft (Version 2)
5 Week Modular Course in Statistics & Probability Strand 1 Module 4 Set Theory and Probability It is often said that the three basic rules of probability are: 1. Draw a picture 2. Draw a picture 3. Draw
More informationProbability GCSE MATHS. Name: Teacher: By the end this pack you will be able to: 1. Find probabilities on probability scales
Probability GCSE MATHS Name: Teacher: Learning objectives By the end this pack you will be able to: 1. Find probabilities on probability scales 2. Calculate theoretical probability and relative frequency
More informationA collection of 91 Maths GCSE Sample and Specimen questions from AQA, OCR, PearsonEdexcel and WJEC Eduqas. Name: Total Marks:
Probability 2 (H) A collection of 91 Maths GCSE Sample and Specimen questions from AQA, OCR, PearsonEdexcel and WJEC Eduqas. Name: Total Marks: 1. Andy sometimes gets a lift to and from college. When
More informationProbability. Probabilty Impossibe Unlikely Equally Likely Likely Certain
PROBABILITY Probability The likelihood or chance of an event occurring If an event is IMPOSSIBLE its probability is ZERO If an event is CERTAIN its probability is ONE So all probabilities lie between 0
More informationRevision Topic 17: Probability Estimating probabilities: Relative frequency
Revision Topic 17: Probability Estimating probabilities: Relative frequency Probabilities can be estimated from experiments. The relative frequency is found using the formula: number of times event occurs.
More informationProbability. Ms. Weinstein Probability & Statistics
Probability Ms. Weinstein Probability & Statistics Definitions Sample Space The sample space, S, of a random phenomenon is the set of all possible outcomes. Event An event is a set of outcomes of a random
More information4.1 Sample Spaces and Events
4.1 Sample Spaces and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment is called an
More informationDiamond ( ) (Black coloured) (Black coloured) (Red coloured) ILLUSTRATIVE EXAMPLES
CHAPTER 15 PROBABILITY Points to Remember : 1. In the experimental approach to probability, we find the probability of the occurence of an event by actually performing the experiment a number of times
More informationProbability  Grade 10 *
OpenStaxCNX module: m32623 1 Probability  Grade 10 * Rory Adams Free High School Science Texts Project Sarah Blyth Heather Williams This work is produced by OpenStaxCNX and licensed under the Creative
More information5.6. Independent Events. INVESTIGATE the Math. Reflecting
5.6 Independent Events YOU WILL NEED calculator EXPLORE The Fortin family has two children. Cam determines the probability that the family has two girls. Rushanna determines the probability that the family
More information7.1 Experiments, Sample Spaces, and Events
7.1 Experiments, Sample Spaces, and Events An experiment is an activity that has observable results. Examples: Tossing a coin, rolling dice, picking marbles out of a jar, etc. The result of an experiment
More informationName: Probability, Part 1 March 4, 2013
1) Assuming all sections are equal in size, what is the probability of the spinner below stopping on a blue section? Write the probability as a fraction. 2) A bag contains 3 red marbles, 4 blue marbles,
More informationBefore giving a formal definition of probability, we explain some terms related to probability.
probability 22 INTRODUCTION In our daytoday life, we come across statements such as: (i) It may rain today. (ii) Probably Rajesh will top his class. (iii) I doubt she will pass the test. (iv) It is unlikely
More informationChapter 1: Sets and Probability
Chapter 1: Sets and Probability Section 1.31.5 Recap: Sample Spaces and Events An is an activity that has observable results. An is the result of an experiment. Example 1 Examples of experiments: Flipping
More informationTHOMAS WHITHAM SIXTH FORM
THOMAS WHITHAM SIXTH FORM Handling Data Levels 6 8 S. J. Cooper Probability Tree diagrams & Sample spaces Statistical Graphs Scatter diagrams Mean, Mode & Median Year 9 B U R N L E Y C A M P U S, B U R
More informationI. WHAT IS PROBABILITY?
C HAPTER 3 PROAILITY Random Experiments I. WHAT IS PROAILITY? The weatherman on 10 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and
More informationSTANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving.
Worksheet 4 th Topic : PROBABILITY TIME : 4 X 45 minutes STANDARD COMPETENCY : 1. To use the statistics rules, the rules of counting, and the characteristic of probability in problem solving. BASIC COMPETENCY:
More information1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 100 calculators is tested.
1. A factory makes calculators. Over a long period, 2 % of them are found to be faulty. A random sample of 0 calculators is tested. Write down the expected number of faulty calculators in the sample. Find
More informationDefine and Diagram Outcomes (Subsets) of the Sample Space (Universal Set)
12.3 and 12.4 Notes Geometry 1 Diagramming the Sample Space using Venn Diagrams A sample space represents all things that could occur for a given event. In set theory language this would be known as the
More informationUnit 9: Probability Assignments
Unit 9: Probability Assignments #1: Basic Probability In each of exercises 1 & 2, find the probability that the spinner shown would land on (a) red, (b) yellow, (c) blue. 1. 2. Y B B Y B R Y Y B R 3. Suppose
More informationIndependent Events B R Y
. Independent Events Lesson Objectives Understand independent events. Use the multiplication rule and the addition rule of probability to solve problems with independent events. Vocabulary independent
More informationMath : Probabilities
20 20. Probability EPProgram  Strisuksa School  Roiet Math : Probabilities Dr.Wattana Toutip  Department of Mathematics Khon Kaen University 200 :Wattana Toutip wattou@kku.ac.th http://home.kku.ac.th/wattou
More information2. A bubblegum machine contains 25 gumballs. There are 12 green, 6 purple, 2 orange, and 5 yellow gumballs.
A C E Applications Connections Extensions Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability
More informationProbability Interactives from Spire Maths A Spire Maths Activity
Probability Interactives from Spire Maths A Spire Maths Activity https://spiremaths.co.uk/ia/ There are 12 sets of Probability Interactives: each contains a main and plenary flash file. Titles are shown
More informationMath 1313 Section 6.2 Definition of Probability
Math 1313 Section 6.2 Definition of Probability Probability is a measure of the likelihood that an event occurs. For example, if there is a 20% chance of rain tomorrow, that means that the probability
More informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource Probability D/L. Contents Independent Events D/L. Page  Combined Events D/L. Page  9 West Nottinghamshire College D/L. Information Independent Events
More informationClass XII Chapter 13 Probability Maths. Exercise 13.1
Exercise 13.1 Question 1: Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E F) = 0.2, find P (E F) and P(F E). It is given that P(E) = 0.6, P(F) = 0.3, and P(E F) = 0.2 Question 2:
More informationOn the probability scale below mark, with a letter, the probability that the spinner will land
GCSE Exam Questions on Basic Probability. Richard has a box of toy cars. Each car is red or blue or white. 3 of the cars are red. 4 of the cars are blue. of the cars are white. Richard chooses one car
More informationName: Class: Date: 6. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is 11
Class: Date: Sample Mastery # Multiple Choice Identify the choice that best completes the statement or answers the question.. One repetition of an experiment is known as a(n) random variable expected value
More informationChance and Probability
F Student Book Name Series F Contents Topic Chance and probability (pp. 0) ordering events relating fractions to likelihood chance experiments fair or unfair the mathletics cup create greedy pig solve
More informationProbability. Dr. Zhang Fordham Univ.
Probability! Dr. Zhang Fordham Univ. 1 Probability: outline Introduction! Experiment, event, sample space! Probability of events! Calculate Probability! Through counting! Sum rule and general sum rule!
More informationUnit 1 Day 1: Sample Spaces and Subsets. Define: Sample Space. Define: Intersection of two sets (A B) Define: Union of two sets (A B)
Unit 1 Day 1: Sample Spaces and Subsets Students will be able to (SWBAT) describe events as subsets of sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions,
More informationUnit 7 Central Tendency and Probability
Name: Block: 7.1 Central Tendency 7.2 Introduction to Probability 7.3 Independent Events 7.4 Dependent Events 7.1 Central Tendency A central tendency is a central or value in a data set. We will look at
More informationChapter 1  Set Theory
Midterm review Math 3201 Name: Chapter 1  Set Theory Part 1: Multiple Choice : 1) U = {hockey, basketball, golf, tennis, volleyball, soccer}. If B = {sports that use a ball}, which element would be in
More information, x {1, 2, k}, where k > 0. (a) Write down P(X = 2). (1) (b) Show that k = 3. (4) Find E(X). (2) (Total 7 marks)
1. The probability distribution of a discrete random variable X is given by 2 x P(X = x) = 14, x {1, 2, k}, where k > 0. Write down P(X = 2). (1) Show that k = 3. Find E(X). (Total 7 marks) 2. In a game
More informationepisteme Probability
episteme Probability Problem Set 3 Please use CAPITAL letters FIRST NAME LAST NAME SCHOOL CLASS DATE / / Set 3 1 episteme, 2010 Set 3 2 episteme, 2010 Coin A fair coin is one which is equally likely to
More informationProbability Test Review Math 2. a. What is? b. What is? c. ( ) d. ( )
Probability Test Review Math 2 Name 1. Use the following venn diagram to answer the question: Event A: Odd Numbers Event B: Numbers greater than 10 a. What is? b. What is? c. ( ) d. ( ) 2. In Jason's homeroom
More informationInstructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to include your name and student numbers.
Math 3201 Unit 3 Probability Assignment 1 Unit Assignment Name: Part 1 Selected Response: Instructions: Choose the best answer and shade the corresponding space on the answer sheet provide. Be sure to
More informationThe probability setup
CHAPTER The probability setup.1. Introduction and basic theory We will have a sample space, denoted S sometimes Ω that consists of all possible outcomes. For example, if we roll two dice, the sample space
More informationNotes #45 Probability as a Fraction, Decimal, and Percent. As a result of what I learn today, I will be able to
Notes #45 Probability as a Fraction, Decimal, and Percent As a result of what I learn today, I will be able to Probabilities can be written in three ways:,, and. Probability is a of how an event is to.
More informationSection 7.3 and 7.4 Probability of Independent Events
Section 7.3 and 7.4 Probability of Independent Events Grade 7 Review Two or more events are independent when one event does not affect the outcome of the other event(s). For example, flipping a coin and
More informationSTRAND: PROBABILITY Unit 1 Probability of One Event
STRAND: PROBABILITY Unit 1 Probability of One Event TEXT Contents Section 1.1 Probabilities 1.2 Straightforward Probability 1.3 Finding Probabilities Using Relative Frequency 1.4 Determining Probabilities
More informationPractice Ace Problems
Unit 6: Moving Straight Ahead Investigation 2: Experimental and Theoretical Probability Practice Ace Problems Directions: Please complete the necessary problems to earn a maximum of 12 points according
More informationALL FRACTIONS SHOULD BE IN SIMPLEST TERMS
Math 7 Probability Test Review Name: Date Hour Directions: Read each question carefully. Answer each question completely. ALL FRACTIONS SHOULD BE IN SIMPLEST TERMS! Show all your work for full credit!
More informationCLASSIFIED ALEVEL PROBABILITY S1 BY: MR. AFDZAL Page 1
5 At a zoo, rides are offered on elephants, camels and jungle tractors. Ravi has money for only one ride. To decide which ride to choose, he tosses a fair coin twice. If he gets 2 heads he will go on the
More informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource HD2/L. HD2/L.2 Excellence in skills development Contents HD2/L. Pages 36 HD2/L.2 West Nottinghamshire College 2 HD2/L. HD2/L.2 Information is the
More informationCHAPTER 7 Probability
CHAPTER 7 Probability 7.1. Sets A set is a welldefined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can
More informationThe probability setup
CHAPTER 2 The probability setup 2.1. Introduction and basic theory We will have a sample space, denoted S (sometimes Ω) that consists of all possible outcomes. For example, if we roll two dice, the sample
More informationPLC Papers Created For:
PLC Papers Created For: Year 10 Topic Practice Papers: Probability Mutually Exclusive Sum 1 Grade 4 Objective: Know that the sum of all possible mutually exclusive outcomes is 1. Question 1. Here are some
More informationProbability. Chapter13
Chapter3 Probability The definition of probability was given b Pierre Simon Laplace in 795 J.Cardan, an Italian physician and mathematician wrote the first book on probability named the book of games
More informationQuiz 2 Review  on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II??
Quiz 2 Review  on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n What are the formulas? Pr ncr Fill in the notation
More informationName: Section: Date:
WORKSHEET 5: PROBABILITY Name: Section: Date: Answer the following problems and show computations on the blank spaces provided. 1. In a class there are 14 boys and 16 girls. What is the probability of
More informationChance and Probability
G Student Book Name Series G Contents Topic Chance and probability (pp. ) probability scale using samples to predict probability tree diagrams chance experiments using tables location, location apply lucky
More informationIntermediate Math Circles November 1, 2017 Probability I
Intermediate Math Circles November 1, 2017 Probability I Probability is the study of uncertain events or outcomes. Games of chance that involve rolling dice or dealing cards are one obvious area of application.
More information2. The figure shows the face of a spinner. The numbers are all equally likely to occur.
MYP IB Review 9 Probability Name: Date: 1. For a carnival game, a jar contains 20 blue marbles and 80 red marbles. 1. Children take turns randomly selecting a marble from the jar. If a blue marble is chosen,
More informationSection Introduction to Sets
Section 1.1  Introduction to Sets Definition: A set is a welldefined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
More informationCHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY
CHAPTER 9  COUNTING PRINCIPLES AND PROBABILITY Probability is the Probability is used in many realworld fields, such as insurance, medical research, law enforcement, and political science. Objectives:
More informationPROBABILITY Case of cards
WORKSHEET NO1 PROBABILITY Case of cards WORKSHEET NO2 Case of two die Case of coins WORKSHEET NO3 1) Fill in the blanks: A. The probability of an impossible event is B. The probability of a sure
More informationChance and Probability
Series Student Chance and Probability My name F Copyright 009 P Learning. All rights reserved. First edition printed 009 in Australia. A catalogue record for this book is available from P Learning Ltd.
More informationMath 3201 Unit 3: Probability Name:
Multiple Choice Math 3201 Unit 3: Probability Name: 1. Given the following probabilities, which event is most likely to occur? A. P(A) = 0.2 B. P(B) = C. P(C) = 0.3 D. P(D) = 2. Three events, A, B, and
More information136 Probabilities of Mutually Exclusive Events
Determine whether the events are mutually exclusive or not mutually exclusive. Explain your reasoning. 1. drawing a card from a standard deck and getting a jack or a club The jack of clubs is an outcome
More informationCounting Methods and Probability
CHAPTER Counting Methods and Probability Many good basketball players can make 90% of their free throws. However, the likelihood of a player making several free throws in a row will be less than 90%. You
More informationWhat Do You Expect? Concepts
Important Concepts What Do You Expect? Concepts Examples Probability A number from 0 to 1 that describes the likelihood that an event will occur. Theoretical Probability A probability obtained by analyzing
More informationKS3 Levels 38. Unit 3 Probability. Homework Booklet. Complete this table indicating the homework you have been set and when it is due by.
Name: Maths Group: Tutor Set: Unit 3 Probability Homework Booklet KS3 Levels 38 Complete this table indicating the homework you have been set and when it is due by. Date Homework Due By Handed In Please
More informationName: Period: Date: 7 th PreAP: Probability Review and MiniReview for Exam
Name: Period: Date: 7 th PreAP: Probability Review and MiniReview for Exam 4. Mrs. Bartilotta s mathematics class has 7 girls and 3 boys. She will randomly choose two students to do a problem in front
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Mathematical Ideas Chapter 2 Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) In one town, 2% of all voters are Democrats. If two voters
More informationApplications. 28 How Likely Is It? P(green) = 7 P(yellow) = 7 P(red) = 7. P(green) = 7 P(purple) = 7 P(orange) = 7 P(yellow) = 7
Applications. A bucket contains one green block, one red block, and two yellow blocks. You choose one block from the bucket. a. Find the theoretical probability that you will choose each color. P(green)
More informationA 20% B 25% C 50% D 80% 2. Which spinner has a greater likelihood of landing on 5 rather than 3?
1. At a middle school, 1 of the students have a cell phone. If a student is chosen at 5 random, what is the probability the student does not have a cell phone? A 20% B 25% C 50% D 80% 2. Which spinner
More informationRANDOM EXPERIMENTS AND EVENTS
Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In daytoday life we see that before commencement of a cricket match two captains go for a toss. Tossing of a coin is an activity and getting
More information1. Decide whether the possible resulting events are equally likely. Explain. Possible resulting events
Applications. Decide whether the possible resulting events are equally likely. Explain. Action Possible resulting events a. You roll a number You roll an even number, or you roll an cube. odd number. b.
More informationRelative frequency and probability
5 Relative frequency and probability Syllabus topic MSS Relative frequency and probability This topic will develop your awareness of the broad range of applications of probability concepts in everyday
More informationPRE TEST KEY. Math in a Cultural Context*
PRE TEST KEY Salmon Fishing: Investigations into A 6 th grade module in the Math in a Cultural Context* UNIVERSITY OF ALASKA FAIRBANKS Student Name: PRE TEST KEY Grade: Teacher: School: Location of School:
More informationSECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability
SECONDARY 2 Honors ~ Lesson 9.2 Worksheet Intro to Probability Name Period Write all probabilities as fractions in reduced form! Use the given information to complete problems 13. Five students have the
More informationUnit 11 Probability. Round 1 Round 2 Round 3 Round 4
Study Notes 11.1 Intro to Probability Unit 11 Probability Many events can t be predicted with total certainty. The best thing we can do is say how likely they are to happen, using the idea of probability.
More informationChapterwise questions. Probability. 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail.
Probability 1. Two coins are tossed simultaneously. Find the probability of getting exactly one tail. 2. 26 cards marked with English letters A to Z (one letter on each card) are shuffled well. If one
More informationOutcomes: The outcomes of this experiment are yellow, blue, red and green.
(Adapted from http://www.mathgoodies.com/) 1. Sample Space The sample space of an experiment is the set of all possible outcomes of that experiment. The sum of the probabilities of the distinct outcomes
More informationWhen a number cube is rolled once, the possible numbers that could show face up are
C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that
More informationD1 Probability of One Event
D Probability of One Event Year 3/4. I have 3 bags of marbles. Bag A contains 0 marbles, Bag B contains 20 marbles and Bag C contains 30 marbles. One marble in each bag is red. a) Join up each statement
More informationUse a tree diagram to find the number of possible outcomes. 2. How many outcomes are there altogether? 2.
Use a tree diagram to find the number of possible outcomes. 1. A pouch contains a blue chip and a red chip. A second pouch contains two blue chips and a red chip. A chip is picked from each pouch. The
More informationheads 1/2 1/6 roll a die sum on 2 dice 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 1, 2, 3, 4, 5, 6 heads tails 3/36 = 1/12 toss a coin trial: an occurrence
trial: an occurrence roll a die toss a coin sum on 2 dice sample space: all the things that could happen in each trial 1, 2, 3, 4, 5, 6 heads tails 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 example of an outcome:
More informationSection 7.1 Experiments, Sample Spaces, and Events
Section 7.1 Experiments, Sample Spaces, and Events Experiments An experiment is an activity with observable results. 1. Which of the follow are experiments? (a) Going into a room and turning on a light.
More informationP(H and H) 5 1_. The probability of picking the ace of diamonds from a pack of cards is 1
Probability Links to: Middle Student Book h, pp.xx xx Key Points alculating the probability an event does not happen ( Probability that an event will not happen ) ( Mutually exclusive events Probability
More informationMethods in Mathematics
Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 1: Methods 1 For Approved Pilot Centres ONLY Foundation Tier Monday 17 June 2013 Morning
More informationStat210 WorkSheet#2 Chapter#2
1. When rolling a die 5 times, the number of elements of the sample space equals.(ans.=7,776) 2. If an experiment consists of throwing a die and then drawing a letter at random from the English alphabet,
More informationMutually Exclusive Events Algebra 1
Name: Mutually Exclusive Events Algebra 1 Date: Mutually exclusive events are two events which have no outcomes in common. The probability that these two events would occur at the same time is zero. Exercise
More information