Fdaytalk.com. Outcomes is probable results related to an experiment
|
|
- Shonda Short
- 6 years ago
- Views:
Transcription
1 EXPERIMENT: Experiment is Definite/Countable probable results Example: Tossing a coin Throwing a dice OUTCOMES: Outcomes is probable results related to an experiment Example: H, T Coin 1, 2, 3, 4, 5, 6 Dice SAMPLE SPACE: Sample space is total no. of outcomes/set of all possible outcomes related to an experiment Example: { H, T } { 1, 2, 3, 4, 5, 6 } PROBABILITY OF AN EVENT [ P(E) ]: P(E) No. of favourable outcomes SURE EVENT: Total no. of outcomes No. of favourable outcomes No.of total outcomes P(E) 1 IMPOSSIBLE EVENT: 1 No outcome satisfies the event i. e P(E) 0 COMPLEMENTARY EVENT [ P(E) ]: P(E ) 1 P(E) i. e P(E) + P(E ) 1 0 P(E) 1 SAMPLE SPACE: 1 Tossing one coin 2 { H, T } 2 Tossing two coins { HT, TH, HH, TT } 3 Tossing three coins { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } 4 Tossing four coins { } 5 Tossing/throwing a Dice 6 { 1, 2, 3, 4, 5, 6 } 6 Tossing/throwing two Dice { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) } 7 Tossing/throwing three Dice { }
2 8 Throwing a Coin & Dice together PACK OF CARDS (PLAYING CARDS): Total playing cards 52 Total different cards (13) Ace (A) Jack (J) Queen (Q) King (K) 52 playing cards divided into 4 sets Hearts 13 cards Red color Diamonds 13 cards Red color Spades 13 cards Black color Clubs 13 cards Black color FACE CARDS: Jacks, Queens and Kings are called Face Cards because the cards pictures of their names There are 12 face cards n cr n! (n r)! r! n cr n cn r n cn 1 n c C2 10! (10 2)! 2! 10! 8! 2! ! 8! (answer) 1 A bag contains 6 white, 4 black balls. Two balls are drawn at a random. Find the possibility that they are the same color. n(s) C2 N(E) (2 white balls out of 6) or (2 black ball out of 4)
3 6 C2 + 4 C2 21 Therefore, P(E) (answer) 2 A card is drawn from a pack of 52 cards. The probability of getting a queen of club or king of heart is.. N(S) 52 Let E event of getting a queen of club or king of heart Then, N(E) 2 Therefore, P(E) (answer) 3 One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either red or a king.. N(s) 52 There are 26 red cards (including 2 kings) & there are two more kings Let E event of getting a red car or king N(E) 28 Therefore, P(E) (answer) 4 A box contains 5 green, 4 yellows and 3 white marbles. 3 marbles are drawn random. What is the probability that they are not the same color.. N(S) C3 220 Let E event of drawing (3 marbles out of 5) or (3 marbles out of 4) or (3 marbles out of 3) 5 C2 + 4 C2 + 3 C2 15
4 Therefore, P(E) 15 / (answer) 44 5 A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the ball drawn is blue N(S) C2 21 Let N(E) No. of ways drawing 2 ballsout oof (2+3) 5 C2 10 Therefore, P(E) (answer) 6 A box contains 4 green, 3 red and 6 blue pens. If two pens are picked at random. What is the probability that they are different color. Total no. of ways 2 pens selected from the 13 (4+3+6) pens N(S) 13 C2 78 No. of ways two different colour pes are selected is P(E) 4 C1 3 C1 + 3 C1 6 C1 + 6 C1 4 C1 54 Therefore, P(E) (answer) 7 In a lottery 10,000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize if you buy one ticket.. Probability of winning on buying one lottery ticket 10 C C
5 Therefore, required probability (answer) 1000 Fdaytalk.com 8 A speaks the truth 3 out of 4 times and B, 5 out of 6 times. What is the probability that they will contradict each other in starting the same fact. The probability that A speaks truth 3 4 The probability that A lies The probability that B speaks truth 5 6 The probability that B lies Both are contradictory, therefore, one will speak truth and other lie Therefore, required probability (answer) 9 In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize (getting a prize) (answer) 7 10 If the probability of police ride on any given day in the house of a criminal is 50%, then what is the probability that is the police raid on exactly 3 days in 5 day period Probability that the house could be raided on any day in 5 days period C (answer) 11 Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that both of them are either red or king..
6 26 C C2 2 C2 52 C (answer) 12 A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9. The no. of numbers whose sum is 9 One digit numbers 1 Two digit numbers 9 Three digit numbers Therefore, required probability (answer) 13 A company CEO wants to visit four plants P, Q, R and S on the official trip. The probability that he visits Q just before R is Let QR as one unit 3! 4! 1 4 (answer) 14 Four boys and three girls stand in queue for an interview. The probability that they stand in alternate position is.. Total no. of possible arrangements for 4- boys and 3- girls in a queue 7! When they occupy alternate position, then the arrangement would be like BGBGBGB Thus, total no. of possible arrangements 4! 3! Therefore, required probability 4! 3! 7! 1 35 (answer) 15 The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3. The probability that none of them will be alive for 10 more years is
7 (1 1 4 ) (1 1 3 ) 1 2 (answer) 16 Ram and Shyam appear for an interview for two vacancies in an organization for the same post. The probabilities of their selection are 1 6 and 2 5 respectively. What is the probability that at least one of them will be selected? 1 (1 1 6 ) (1 2 5 ) (Answer) 17 A person has 12 friends of whom 8 are relatives. In how many ways can he invite 7 friends such that at least 5 of them may be relatives? No. of ways 8c 5 4c 2 + 8c 6 4c 1 + 8c (answer) P, Q and R shoot to hit a target. If P hits the target 4 times in 5 trials, Q hits it 3 times in 4 trials and R hits it 2 times in 3 trials. What is the probability that the target is hit by at least 2 persons? P 4 5 and P 1 5 Q 3 4 and Q 1 4 R 2 3 and R 1 3 PQR + PQ R + P QR + PQR (answer)
8 18 Two dice are thrown simultaneously. The Probability of obtaining a total score of seven is. Favourable conditions are (6, 1), (5, 2), (4, 3), (3, 4), (2, 5), (1, 6) Total possible cases are Favourable cases Required Probability Total possible cases (answer) 19 In a container there are 28 eggs out of which 8 eggs are rotten. If two eggs are chosen at random, what will be the probability that atleast one egg is rotten. Required combination (1 rotten egg and 1 good egg) or (2 rotten eggs) 8 C1 20 C1 + 8 C C (answer)
Diamond ( ) (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 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 informationPROBABILITY Case of cards
WORKSHEET NO--1 PROBABILITY Case of cards WORKSHEET NO--2 Case of two die Case of coins WORKSHEET NO--3 1) Fill in the blanks: A. The probability of an impossible event is B. The probability of a sure
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 informationProbability Exercise 2
Probability Exercise 2 1 Question 9 A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will
More informationExercise Class XI Chapter 16 Probability Maths
Exercise 16.1 Question 1: Describe the sample space for the indicated experiment: A coin is tossed three times. A coin has two faces: head (H) and tail (T). When a coin is tossed three times, the total
More informationProbability and Statistics. Copyright Cengage Learning. All rights reserved.
Probability and Statistics Copyright Cengage Learning. All rights reserved. 14.2 Probability Copyright Cengage Learning. All rights reserved. Objectives What Is Probability? Calculating Probability by
More informationBefore giving a formal definition of probability, we explain some terms related to probability.
probability 22 INTRODUCTION In our day-to-day 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 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 informationSTAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes
STAT 430/510 Probability Lecture 3: Space and Event; Sample Spaces with Equally Likely Outcomes Pengyuan (Penelope) Wang May 25, 2011 Review We have discussed counting techniques in Chapter 1. (Principle
More informationRANDOM EXPERIMENTS AND EVENTS
Random Experiments and Events 18 RANDOM EXPERIMENTS AND EVENTS In day-to-day 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 informationChapter 8: Probability: The Mathematics of Chance
Chapter 8: Probability: The Mathematics of Chance Free-Response 1. A spinner with regions numbered 1 to 4 is spun and a coin is tossed. Both the number spun and whether the coin lands heads or tails is
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 informationUNIT 4 APPLICATIONS OF PROBABILITY Lesson 1: Events. Instruction. Guided Practice Example 1
Guided Practice Example 1 Bobbi tosses a coin 3 times. What is the probability that she gets exactly 2 heads? Write your answer as a fraction, as a decimal, and as a percent. Sample space = {HHH, HHT,
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 informationQ1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together.
Required Probability = where Q1) 6 boys and 6 girls are seated in a row. What is the probability that all the 6 gurls are together. Solution: As girls are always together so they are considered as a group.
More informationLesson 10: Using Simulation to Estimate a Probability
Lesson 10: Using Simulation to Estimate a Probability Classwork In previous lessons, you estimated probabilities of events by collecting data empirically or by establishing a theoretical probability model.
More informationProbability. Chapter-13
Chapter-3 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 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 informationProbability Assignment
Name Probability Assignment Student # Hr 1. An experiment consists of spinning the spinner one time. a. How many possible outcomes are there? b. List the sample space for the experiment. c. Determine the
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 informationChapter 4: Introduction to Probability
MTH 243 Chapter 4: Introduction to Probability Suppose that we found that one of our pieces of data was unusual. For example suppose our pack of M&M s only had 30 and that was 3.1 standard deviations below
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 informationChapter 16. Probability. For important terms and definitions refer NCERT text book. (6) NCERT text book page 386 question no.
Chapter 16 Probability For important terms and definitions refer NCERT text book. Type- I Concept : sample space (1)NCERT text book page 386 question no. 1 (*) (2) NCERT text book page 386 question no.
More informationGrade 6 Math Circles Fall Oct 14/15 Probability
1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 6 Math Circles Fall 2014 - Oct 14/15 Probability Probability is the likelihood of an event occurring.
More informationXXII Probability. 4. The odds of being accepted in Mathematics at McGill University are 3 to 8. Find the probability of being accepted.
MATHEMATICS 20-BNJ-05 Topics in Mathematics Martin Huard Winter 204 XXII Probability. Find the sample space S along with n S. a) The face cards are removed from a regular deck and then card is selected
More informationChapter-wise 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 informationProbability of Independent and Dependent Events
706 Practice A Probability of In and ependent Events ecide whether each set of events is or. Explain your answer.. A student spins a spinner and rolls a number cube.. A student picks a raffle ticket from
More informationSection 5.4 Permutations and Combinations
Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to
More informationCS 361: Probability & Statistics
January 31, 2018 CS 361: Probability & Statistics Probability Probability theory Probability Reasoning about uncertain situations with formal models Allows us to compute probabilities Experiments will
More informationMath 146 Statistics for the Health Sciences Additional Exercises on Chapter 3
Math 46 Statistics for the Health Sciences Additional Exercises on Chapter 3 Student Name: Find the indicated probability. ) If you flip a coin three times, the possible outcomes are HHH HHT HTH HTT THH
More informationSection 5.4 Permutations and Combinations
Section 5.4 Permutations and Combinations Definition: n-factorial For any natural number n, n! = n( n 1)( n 2) 3 2 1. 0! = 1 A combination of a set is arranging the elements of the set without regard to
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 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 informationMATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #1 - SPRING DR. DAVID BRIDGE
MATH 205 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM # - SPRING 2006 - DR. DAVID BRIDGE TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Tell whether the statement is
More information= = 0.1%. On the other hand, if there are three winning tickets, then the probability of winning one of these winning tickets must be 3 (1)
MA 5 Lecture - Binomial Probabilities Wednesday, April 25, 202. Objectives: Introduce combinations and Pascal s triangle. The Fibonacci sequence had a number pattern that we could analyze in different
More informationFALL 2012 MATH 1324 REVIEW EXAM 4
FALL 01 MATH 134 REVIEW EXAM 4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the sample space for the given experiment. 1) An ordinary die
More informationHomework #1-19: Use the Counting Principle to answer the following questions.
Section 4.3: Tree Diagrams and the Counting Principle Homework #1-19: Use the Counting Principle to answer the following questions. 1) If two dates are selected at random from the 365 days of the year
More informationPROBABILITY Introduction
PROBABILITY 295 PROBABILITY 15 The theory of probabilities and the theory of errors now constitute a formidable body of great mathematical interest and of great practical importance. 15.1 Introduction
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 informationName: Class: Date: Probability/Counting Multiple Choice Pre-Test
Name: _ lass: _ ate: Probability/ounting Multiple hoice Pre-Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1 The dartboard has 8 sections of equal area.
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 informationHARDER PROBABILITY. Two events are said to be mutually exclusive if the occurrence of one excludes the occurrence of the other.
HARDER PROBABILITY MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION LAW OF PROBABILITY Two events are said to be mutually exclusive if the occurrence of one excludes the occurrence of the other. Example Throwing
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 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 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 informationProbability --QUESTIONS-- Principles of Math 12 - Probability Practice Exam 1
Probability --QUESTIONS-- Principles of Math - Probability Practice Exam www.math.com Principles of Math : Probability Practice Exam Use this sheet to record your answers:... 4... 4... 4.. 6. 4.. 6. 7..
More informationProbability. The Bag Model
Probability The Bag Model Imagine a bag (or box) containing balls of various kinds having various colors for example. Assume that a certain fraction p of these balls are of type A. This means N = total
More informationMEP 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 informationBeginnings of Probability I
Beginnings of Probability I Despite the fact that humans have played games of chance forever (so to speak), it is only in the 17 th century that two mathematicians, Pierre Fermat and Blaise Pascal, set
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 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 informationKey Concepts. Theoretical Probability. Terminology. Lesson 11-1
Key Concepts Theoretical Probability Lesson - Objective Teach students the terminology used in probability theory, and how to make calculations pertaining to experiments where all outcomes are equally
More informationPROBABILITY. The sample space of the experiment of tossing two coins is given by
PROBABILITY Introduction Probability is defined as a quantitative measure of uncertainty a numerical value that conveys the strength of our belief in the occurrence of an event. The probability of an event
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 informationEECS 203 Spring 2016 Lecture 15 Page 1 of 6
EECS 203 Spring 2016 Lecture 15 Page 1 of 6 Counting We ve been working on counting for the last two lectures. We re going to continue on counting and probability for about 1.5 more lectures (including
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 informationWorksheets for GCSE Mathematics. Probability. mr-mathematics.com Maths Resources for Teachers. Handling Data
Worksheets for GCSE Mathematics Probability mr-mathematics.com Maths Resources for Teachers Handling Data Probability Worksheets Contents Differentiated Independent Learning Worksheets Probability Scales
More information1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2)
Math 1090 Test 2 Review Worksheet Ch5 and Ch 6 Name Use the following distribution to answer the question. 1) What is the total area under the curve? 1) 2) What is the mean of the distribution? 2) 3) Estimate
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
6. Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the probability. ) A bag contains red marbles, blue marbles, and 8
More informationDeveloped by Rashmi Kathuria. She can be reached at
Developed by Rashmi Kathuria. She can be reached at . Photocopiable Activity 1: Step by step Topic Nature of task Content coverage Learning objectives Task Duration Arithmetic
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 informationClassical vs. Empirical Probability Activity
Name: Date: Hour : Classical vs. Empirical Probability Activity (100 Formative Points) For this activity, you will be taking part in 5 different probability experiments: Rolling dice, drawing cards, drawing
More informationWeek 1: Probability models and counting
Week 1: Probability models and counting Part 1: Probability model Probability theory is the mathematical toolbox to describe phenomena or experiments where randomness occur. To have a probability model
More informationMath June Review: Probability and Voting Procedures
Math - June Review: Probability and Voting Procedures A big box contains 7 chocolate doughnuts and honey doughnuts. A small box contains doughnuts: some are chocolate doughnuts, and the others are honey
More informationSection The Multiplication Principle and Permutations
Section 2.1 - The Multiplication Principle and Permutations Example 1: A yogurt shop has 4 flavors (chocolate, vanilla, strawberry, and blueberry) and three sizes (small, medium, and large). How many different
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 six-sided dice is thrown once. The boxes show some of the possible outcomes. Draw a line from
More informationConditional Probability Worksheet
Conditional Probability Worksheet P( A and B) P(A B) = P( B) Exercises 3-6, compute the conditional probabilities P( AB) and P( B A ) 3. P A = 0.7, P B = 0.4, P A B = 0.25 4. P A = 0.45, P B = 0.8, P A
More informationMath 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8
Math 12 Academic Assignment 9: Probability Outcomes: B8, G1, G2, G3, G4, G7, G8 Name: 45 1. A customer chooses 5 or 6 tapes from a bin of 40. What is the expression that gives the total number of possibilities?
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 informationHere are two situations involving chance:
Obstacle Courses 1. Introduction. Here are two situations involving chance: (i) Someone rolls a die three times. (People usually roll dice in pairs, so dice is more common than die, the singular form.)
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 informationABC High School, Kathmandu, Nepal. Topic : Probability
BC High School, athmandu, Nepal Topic : Probability Grade 0 Teacher: Shyam Prasad charya. Objective of the Module: t the end of this lesson, students will be able to define and say formula of. define Mutually
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 informationSection 6.5 Conditional Probability
Section 6.5 Conditional Probability Example 1: An urn contains 5 green marbles and 7 black marbles. Two marbles are drawn in succession and without replacement from the urn. a) What is the probability
More informationRelative frequency and probability
5 Relative frequency and probability Syllabus topic MS-S Relative frequency and probability This topic will develop your awareness of the broad range of applications of probability concepts in everyday
More informationNormal Distribution Lecture Notes Continued
Normal Distribution Lecture Notes Continued 1. Two Outcome Situations Situation: Two outcomes (for against; heads tails; yes no) p = percent in favor q = percent opposed Written as decimals p + q = 1 Why?
More informationThis Probability Packet Belongs to:
This Probability Packet Belongs to: 1 2 Station #1: M & M s 1. What is the sample space of your bag of M&M s? 2. Find the theoretical probability of the M&M s in your bag. Then, place the candy back into
More informationSTOR 155 Introductory Statistics. Lecture 10: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 10: Randomness and Probability Model 10/6/09 Lecture 10 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationConditional Probability Worksheet
Conditional Probability Worksheet EXAMPLE 4. Drug Testing and Conditional Probability Suppose that a company claims it has a test that is 95% effective in determining whether an athlete is using a steroid.
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 information12 Probability. Introduction Randomness
2 Probability Assessment statements 5.2 Concepts of trial, outcome, equally likely outcomes, sample space (U) and event. The probability of an event A as P(A) 5 n(a)/n(u ). The complementary events as
More informationProbability - Grade 10 *
OpenStax-CNX module: m32623 1 Probability - Grade 10 * Rory Adams Free High School Science Texts Project Sarah Blyth Heather Williams This work is produced by OpenStax-CNX and licensed under the Creative
More informationProbability: Part 1 1/28/16
Probability: Part 1 1/28/16 The Kind of Studies We Can t Do Anymore Negative operant conditioning with a random reward system Addictive behavior under a random reward system FBJ murine osteosarcoma viral
More information6. In how many different ways can you answer 10 multiple-choice questions if each question has five choices?
Pre-Calculus Section 4.1 Multiplication, Addition, and Complement 1. Evaluate each of the following: a. 5! b. 6! c. 7! d. 0! 2. Evaluate each of the following: a. 10! b. 20! 9! 18! 3. In how many different
More informationLesson 3 Dependent and Independent Events
Lesson 3 Dependent and Independent Events When working with 2 separate events, we must first consider if the first event affects the second event. Situation 1 Situation 2 Drawing two cards from a deck
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 informationb. 2 ; the probability of choosing a white d. P(white) 25, or a a. Since the probability of choosing a
Applications. a. P(green) =, P(yellow) = 2, or 2, P(red) = 2 ; three of the four blocks are not red. d. 2. a. P(green) = 2 25, P(purple) = 6 25, P(orange) = 2 25, P(yellow) = 5 25, or 5 2 6 2 5 25 25 25
More informationTEST A CHAPTER 11, PROBABILITY
TEST A CHAPTER 11, PROBABILITY 1. Two fair dice are rolled. Find the probability that the sum turning up is 9, given that the first die turns up an even number. 2. Two fair dice are rolled. Find the probability
More informationChapter 3: PROBABILITY
Chapter 3 Math 3201 1 3.1 Exploring Probability: P(event) = Chapter 3: PROBABILITY number of outcomes favourable to the event total number of outcomes in the sample space An event is any collection of
More informationProbability Rules. 2) The probability, P, of any event ranges from which of the following?
Name: WORKSHEET : Date: Answer the following questions. 1) Probability of event E occurring is... P(E) = Number of ways to get E/Total number of outcomes possible in S, the sample space....if. 2) The probability,
More informationUNCORRECTED SAMPLE PAGES
1 1A 12 Probability Probability arises when we perform an experiment that has various possible outcomes, but there is insufficient information to predict which of these outcomes will occur. The classic
More informationProbability Review 41
Probability Review 41 For the following problems, give the probability to four decimals, or give a fraction, or if necessary, use scientific notation. Use P(A) = 1 - P(not A) 1) A coin is tossed 6 times.
More informationSTAT 155 Introductory Statistics. Lecture 11: Randomness and Probability Model
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 11: Randomness and Probability Model 10/5/06 Lecture 11 1 The Monty Hall Problem Let s Make A Deal: a game show
More informationECON 214 Elements of Statistics for Economists
ECON 214 Elements of Statistics for Economists Session 4 Probability Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education School of Continuing
More informationFinite Mathematics MAT 141: Chapter 8 Notes
Finite Mathematics MAT 4: Chapter 8 Notes Counting Principles; More David J. Gisch The Multiplication Principle; Permutations Multiplication Principle Multiplication Principle You can think of the multiplication
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 informationAlgebra I Notes Unit One: Real Number System
Syllabus Objectives: 1.1 The student will organize statistical data through the use of matrices (with and without technology). 1.2 The student will perform addition, subtraction, and scalar multiplication
More informationContents 2.1 Basic Concepts of Probability Methods of Assigning Probabilities Principle of Counting - Permutation and Combination 39
CHAPTER 2 PROBABILITY Contents 2.1 Basic Concepts of Probability 38 2.2 Probability of an Event 39 2.3 Methods of Assigning Probabilities 39 2.4 Principle of Counting - Permutation and Combination 39 2.5
More informationCSC/MTH 231 Discrete Structures II Spring, Homework 5
CSC/MTH 231 Discrete Structures II Spring, 2010 Homework 5 Name 1. A six sided die D (with sides numbered 1, 2, 3, 4, 5, 6) is thrown once. a. What is the probability that a 3 is thrown? b. What is the
More information