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1 PAGES 4-5 KEY Organize the data into the circles. A. Factors of 64: 1, 2, 4, 8, 16, 32, 64 B. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 A B Answer Questions about the diagram below Fall Sports Winter Sports Spring Sports 1) How many students play sports year-round? 3 2) How many students play sports only in the spring and fall? 6 3) How many students play sports only in the winter and fall? 13 4) How many students play sports only in the winter and spring? 2 5) How many students play only one sport? 48 6) How many students play at least two sports? 24

2 7) Suppose you have a standard deck of 52 cards. Let: a. Describe for this experiment, and find the probability of. A B = {7 spades, 7 clubs, 7 hearts, all diamonds} P(A B) = 16/52 or 4/13 b. Describe for this experiment, and find the probability of. A B = {7 diamonds} P(A B) = 1/52 8) Suppose a box contains three balls, one red, one blue, and one white. One ball is selected, its color is observed, and then the ball is placed back in the box. The balls are scrambled, and again, a ball is selected and its color is observed. What is the sample space of the experiment? S = {RR, RB, RW, BR, BB, BW, WR, WB, WW} 9) Suppose you have a jar of candies: 4 red, 5 purple and 7 green. Find the following probabilities of the following events: Selecting a red candy. 1/4 Selecting a purple candy. 5/16 Selecting a green or red candy. 11/16 Selecting a yellow candy. 0 Selecting any color except a green candy. 9/16 Find the odds of selecting a red candy. 7/9 Find the odds of selecting a purple or green candy. 9/7 10) What is the sample space for a single spin of a spinner with red, blue, yellow and green sections spinner? {red, blue, yellow, green} What is the sample space for 2 spins of the first spinner? {RR, RB, RY, RG, BR, BB, BY, BG, YR, YB, YY, YG, GR, GB, GY, GG} If the spinner is equally likely to land on each color, what is the probability of landing on red in one spin? 1/4 What is the probability of landing on a primary color in one spin? 3/4 What is the probability of landing on green both times in two spins? 1/16 11) Consider the throw of a die experiment. Assume we define the following events: Describe for this experiment. {1,2,3,4,6} Describe for this experiment. {2} Calculate and, assuming the die is fair. 5/6 1/6

3 PAGES KEY Independent and Dependent Events 1. Determine which of the following are examples of independent or dependent events. a. Rolling a 5 on one die and rolling a 5 on a second die. independent b. Choosing a cookie from the cookie jar and choosing a jack from a deck of cards. Indepen. c. Selecting a book from the library and selecting a book that is a mystery novel. Dependent d. Going to the beach and bringing an umbrella. Dependent e. Getting gasoline for your car and getting diesel fuel for your car. dependent f. Choosing an 8 from a deck of cards, replacing it, and choosing a face card. Indepen. g. Choosing a jack from a deck of cards and choosing another jack, without replacement. dependent h. Being lunchtime and eating a sandwich. dependent 2. A coin and a die are tossed. Calculate the probability of getting tails and a 5. 1/12 3. In Tania's homeroom class, 9% of the students were born in March and 40% of the students have a blood type of O+. What is the probability of a student chosen at random from Tania's homeroom class being born in March and having a blood type of O+?.036 or 3.6% 4. If a baseball player gets a hit in 31% of his at-bats, what it the probability that the baseball player will get a hit in 5 at-bats in a row?.0029 or.29% 5. What is the probability of tossing 2 coins one after the other and getting 1 head and 1 tail? 1/ cards are chosen from a deck of cards. The first card is replaced before choosing the second card. What is the probability that they both will be clubs? 1/ cards are chosen from a deck of cards. The first card is replaced before choosing the second card. What is the probability that they both will be face cards? 9/ If the probability of receiving at least 1 piece of mail on any particular day is 22%, what is the probability of not receiving any mail for 3 days in a row? P(not receiving mail) = =.78. P(no mail for 3 days) = (.78)(.78)(.78) =.475 or 47.5% 9. Johnathan is rolling 2 dice and needs to roll an 11 to win the game he is playing. What is the probability that Johnathan wins the game? 2/6 x 1/6 = 1/ Thomas bought a bag of jelly beans that contained 10 red jelly beans, 15 blue jelly beans, and 12 green jelly beans. What is the probability of Thomas reaching into the bag and pulling out a blue or green jelly bean and then reaching in again and pulling out a red jelly bean? Assume that the first jelly bean is not replaced. 27/37 x 10/36 = 15/74

4 11. For question 10, what if the order was reversed? In other words, what is the probability of Thomas reaching into the bag and pulling out a red jelly bean and then reaching in again and pulling out a blue or green jelly bean without replacement? 10/37 x 27/36 = 15/74; same 12. What is the probability of drawing 2 face cards one after the other from a standard deck of cards without replacement? 12/52 x 11/51 = 11/ There are 3 quarters, 7 dimes, 13 nickels, and 27 pennies in Jonah's piggy bank. If Jonah chooses 2 of the coins at random one after the other, what is the probability that the first coin chosen is a nickel and the second coin chosen is a quarter? Assume that the first coin is not replaced. 13/50 x 3/49 = 39/2450 or For question 13, what is the probability that neither of the 2 coins that Jonah chooses are dimes? Assume that the first coin is not replaced. 43/50 x 42/49 = 129/ Jenny bought a half-dozen doughnuts, and she plans to randomly select 1 doughnut each morning and eat it for breakfast until all the doughnuts are gone. If there are 3 glazed, 1 jelly, and 2 plain doughnuts, what is the probability that the last doughnut Jenny eats is a jelly doughnut? 5/6 x 4/5 x 3/4 x 2/3 x 1/2 x 1 = 1/6 16. Steve will draw 2 cards one after the other from a standard deck of cards without replacement. What is the probability that his 2 cards will consist of a heart and a diamond? 13/52 x 13/51 = 13/204

6 15. What is the probability of choosing a number from 1 to 10 that is greater than 5 or even? 5/10 + 5/10 3/10 = 7/ A bag contains 26 tiles with a letter on each, one tile for each letter of the alphabet. What is the probability of reaching into the bag and randomly choosing a tile with one of the letters in the word ENGLISH on it or randomly choosing a tile with a vowel on it? 7/26 + 5/26 2/26 = 10/26 or 5/ Are randomly choosing a teacher and randomly choosing a father mutually inclusive events? Explain your answer. Yes, some teachers are also fathers. 18. Suppose 2 events are mutually inclusive events. If one of the events is passing a test, what could the other event be? Explain your answer. Answers will vary. One answer could be getting an A on the test.

7 PAGES KEY Conditional Probability 1. Compete the following table using sums from rolling two dice. Us e the table to answer questions fair dice are rolled. What is the probability that the sum is even given that the first die that is rolled is a 2? 1/ fair dice are rolled. What is the probability that the sum is even given that the first die rolled is a 5? 1/ fair dice are rolled. What is the probability that the sum is odd given that the first die rolled is a 5? 1/2 5. Steve and Scott are playing a game of cards with a standard deck of playing cards. Steve deals Scott a black king. What is the probability that Scott s second card will be a red card? 26/51 6. Sandra and Karen are playing a game of cards with a standard deck of playing cards. Sandra deals Karen a red seven. What is the probability that Karen s second card will be a black card? 26/51 7. Donna discusses with her parents the idea that she should get an allowance. She says that in her class, 55% of her classmates receive an allowance for doing chores, and 25% get an allowance for doing chores and are good to their parents. Her mom asks Donna what the probability is that a classmate will be good to his or her parents given that he or she receives an allowance for doing chores. What should Donna's answer be?.25/.55 = 45.5% 8. At a local high school, the probability that a student speaks English and French is 15%. The probability that a student speaks French is 45%. What is the probability that a student speaks English, given that the student speaks French?.15/.45 = 33.3% 9. On a game show, there are 16 questions: 8 easy, 5 medium-hard, and 3 hard. If contestants are given questions randomly, what is the probability that the first two contestants will get easy questions? P(2 nd is easy 1 st is easy) = 1/2 10. On the game show above, what is the probability that the first contestant will get an easy question and the second contestant will get a hard question? P(2 nd is hard 1 st is easy) = 1/5 11. Figure 2.2 shows the counts of earned degrees for several colleges on the East Coast. The level of degree and the gender of the degree recipient were tracked. Row & Column totals are included.

8 a. What is the probability that a randomly selected degree recipient is a female? 714/1375 = 51.9% b. What is the probability that a randomly chosen degree recipient is a man? 661/1375 = 48.1% c. What is the probability that a randomly selected degree recipient is a woman, given that they received a Master's Degree? 128/293 = 43.7% d. For a randomly selected degree recipient, what is P(Bachelor's Degree Male)? 438/661 = 66.3% 12. Animals on the endangered species list are given in the table below by type of animal and whether it is domestic or foreign to the United States. Complete the table and answer the following questions. Mammals Birds Reptiles Amphibians Total United States Foreign Total An endangered animal is selected at random. What is the probability that it is: a. a bird found in the United States? 78/663 = 11.8% b. foreign or a mammal? 498/ / /663 = 84.6% c. a bird given that it is found in the United States? 14/165 = 8.5% d. a bird given that it is foreign? 175/498 = 35.1%

9 PAGES 25 KEY Permutations and Combinations For 1-5, find the number of permutations , How many ways can you plant a rose bush, a lavender bush and a hydrangea bush in a row? 6 5. How many ways can you pick a president, a vice president, a secretary and a treasurer out of 28 people for student council? 491,400 For 6-10, find the probabilities. 6. What is the probability that a randomly generated arrangement of the letters A,E,L, Q and U will result in spelling the word EQUAL? What is the probability that a randomly generated 3-letter arrangement of the letters in the word SPIN ends with the letter N? A bag contains ten chips numbered 0 through 9. Two chips are drawn randomly from the bag and laid down in the order they were drawn. What is the probability that the 2-digit number formed is divisible by 3? 33/ 10 P 2 = 11/30 9. A prepaid telephone calling card comes with a randomly selected 4-digit PIN, using the digits 1 through 9 without repeating any digits. What is the probability that the PIN for a card chosen at random does not contain the number 7? (8*7*6*5)/ 9 P 4 = 5/9 10. Janine makes a playlist of 8 songs and has her computer randomly shuffle them. If one song is by Little Bow Wow, what is the probability that this song will play first? 1/8 For 11-13, calculate the number of combinations: For 14-18, a town lottery requires players to choose three different numbers from the numbers 1 through How many different combinations are there? What is the probability that a player s numbers match all three numbers chosen by the computer? 1/ What is the probability that two of a player s numbers match the numbers chosen by the computer? 1/50,979, What is the probability that one of a player s numbers matches the numbers chosen by the computer? 1/ What is the probability that none of a player s numbers match the numbers chosen by the computer? 31/ Looking at the odds that you came up with in question 14, devise a sensible payout plan for the lottery in other words, how big should the prizes be for players who match 1, 2, or all 3 numbers? Assume that tickets cost \$1. Don t forget to take into account the following: a. The town uses the lottery to raise money for schools and sports clubs. b. Selling tickets costs the town a certain amount of money. c. If payouts are too low, nobody will play! Answers will vary.

10 PAGES KEY Investigation: Theoretical vs. Experimental Probability Part 1: Theoretical Probability Probability is the chance or likelihood of an event occurring. We will study two types of probability, theoretical and experimental. Theoretical Probability: the probability of an event is the ratio or the number of favorable outcomes to the total possible outcomes. P(Event) = Number or favorable outcomes Total possible outcomes Sample Space: The set of all possible outcomes. For example, the sample space of tossing a coin is {Heads, Tails} because these are the only two possible outcomes. Theoretical probability is based on the set of all possible outcomes, or the sample space. 1. List the sample space for rolling a six-sided die (remember you are listing a set, so you should use brackets {} ): {1,2,3,4,5,6} Find the following probabilities: P(2) 1/6 P(3 or 6) 1/3 P(odd) 1/2 P(not a 4) 5/6 P(1,2,3,4,5, or 6) 1 P(8) 0 2. List the sample space for tossing two coins: {(H,H), (H,T), (T,H), (T,T)} Find the following probabilities: P(two heads) 1/4 P(one head and one tail) 1/2 P(head, then tail) 1/4 P(all tails) 1/4 P(no tails) 1/4 3. Complete the sample space for tossing two six-sided dice: {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)} Find the following probabilities: P(a 1 and a 4) 1/18 P(a 1, then a 4) 1/36 P(sum of 8) 5/36 P(sum of 12) 1/36 P(doubles) 1/6 P(sum of 15) 0 4. When would you expect the probability of an event occurring to be 1, or 100%? Describe an event whose probability of occurring is 1. Any event that will definitely happen will have a probability of 1. Ex: rolling a 1,2,3,4,5,or 6 on die. 5. When would you expect the probability of an event occurring to be 0, or 0%? Describe an event whose probability of occurring is 0.

12 Click Roll. Notice that there will be a bar on the graph at the right. What does this represent? Now push +1 nine more times. Push the right arrow to see the frequency of each number on the die. How many times did you get a 1? A 2? A 5? Now press the +1, +10, and +50 buttons until you have rolled 100 times. Based on the data, find the following experimental probabilities: P(2) P(3 or 6) P(odd) P(not a 4) Press the +50 button until you have rolled 1000 times. Based on the data, find the following experimental probabilities: P(2) P(3 or 6) P(odd) P(not a 4) Press the +50 button until you have rolled 5000 times. Based on the data, find the following experimental probabilities: P(2) P(3 or 6) P(odd) P(not a 4) What can you expect to happen to the experimental probabilities in the long run? In other words, as the number of trials increases, what happens to the experimental probabilities? As the number of trials increases, the experimental probability should approach the theoretical probability Why can there be differences between experimental and theoretical probabilities in general? Theoretical probabilities tell us what we can expect to happen in the long run. Experimental probability is dependent on the number of trials conducted. Also, just because we know how often something should occur, that does not mean it actually will occur.

13 Part 3: Which one do I use? So when do we use theoretical probability or experimental probability? Theoretical probability is always the best choice, when it can be calculated. But sometimes it is not possible to calculate theoretical probabilities because we cannot possible know all of the possible outcomes. In these cases, experimental probability is appropriate. For example, if we wanted to calculate the probability of a student in the class having green as his or her favorite color, we could not use theoretical probability. We would have to collect data on the favorite colors of each member of the class and use experimental probability. Determine whether theoretical or experimental probability would be appropriate for each of the following. Explain your reasoning: 1. What is the probability of someone tripping on the stairs today between first and second periods? Experimental. We would need to collect data on the total number of students on the stairs between first and second period and how many of those students tripped. 2. What is the probability of rolling a 3 on a six-sided die, then tossing a coin and getting a head? Theoretical. We could list the sample space and find the probability based on the possible outcomes. 3. What is the probability that a student will get 4 of 5 true false questions correct on a quiz? Theoretical. We could list the sample space and find the probability based on the possible outcomes. 4. What is the probability that a student in class is wearing exactly four buttons on his or her clothing today? Experimental. We would have to ask each student how many buttons he or she is wearing to find the probability since we could not possible know all the possible outcomes.

14 PAGES KEY Probability Homework: Experimental vs. Theoretical Name 1) A baseball collector checked 350 cards in case on the shelf and found that 85 of them were damaged. Find the experimental probability of the cards being damaged. Show your work. 85/350 =.24 2) Jimmy rolls a number cube 30 times. He records that the number 6 was rolled 9 times. According to Jimmy's records, what is the experimental probability of rolling a 6? Show your work. 9/30 =.3 3) John, Phil, and Mike are going to a bowling match. Suppose the boys randomly sit in the 3 seats next to each other and one of the seats is next to an aisle. What is the probability that John will sit in the seat next to the aisle? 1/3 4) In Mrs. Johnson's class there are 12 boys and 16 girls. If Mrs. Johnson draws a name at random, what is the probability that the name will be that of a boy? 12/28 =.43 5) Antonia has 9 pairs of white socks and 7 pairs of black socks. Without looking, she pulls a black sock from the drawer. What is the probability that the next sock she pulls out will also be black? 13/31 =.42 (There were 32 socks to start with, but one black sock was removed. That leaves 31 socks, 13 of which are black.) 6) Lenny tosses a nickel 50 times. It lands heads up 32 times and tails 18 times. What is the experimental probability that the nickel lands tails? 18/50 =.36 7) A car manufacturer randomly selected 5,000 cars from their production line and found that 85 had some defects. If 100,000 cars are produced by this manufacturer, how many cars can be expected to have defects? 85/5000 =.017;.017*100,000 = 1700 cars can be expected to have defects. (Source: The following advertisement appeared in the Sunday paper:

15 Chew DentaGum! 4 out of 5 dentists surveyed agree that chewing DentaGum after eating reduces the risk of tooth decay! So enjoy a piece of delicious DentaGum and get fewer cavities! 10 dentists were surveyed. 8) According to the ad, what is the probability that a dentist chosen at random does not agree that chewing DentaGum after meals reduces the risk of tooth decay? 1/5 or.2 9) Is this probability theoretical or experimental? How do you know? Experimental because it is based on a survey or data collected. 10) Do you think that the this advertisement is trying to influence the consumer to buy DentaGum? Why or why not? Yes, the fine print states that only 100 dentists were surveyed. The results may be different if a larger sample was surveyed. 11) What could be done to make this advertisement more believable? The sample of dentists could be made larger. 10 dentists does not give a representative sample of all dentists. The larger the sample, the more accurate the probabilities will be.

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Name: Class: Date: ID: A Chapter 0 Practice Test Probability Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the likelihood of the event given its

### Name Date Class. 2. dime. 3. nickel. 6. randomly drawing 1 of the 4 S s from a bag of 100 Scrabble tiles

Name Date Class Practice A Tina has 3 quarters, 1 dime, and 6 nickels in her pocket. Find the probability of randomly drawing each of the following coins. Write your answer as a fraction, as a decimal,

### Probability and Counting Techniques

Probability and Counting Techniques Diana Pell (Multiplication Principle) Suppose that a task consists of t choices performed consecutively. Suppose that choice 1 can be performed in m 1 ways; for each

### Probability 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.

### Exam 2 Review (Sections Covered: 3.1, 3.3, , 7.1) 1. Write a system of linear inequalities that describes the shaded region.

Exam 2 Review (Sections Covered: 3.1, 3.3, 6.1-6.4, 7.1) 1. Write a system of linear inequalities that describes the shaded region. 5x + 2y 30 x + 2y 12 x 0 y 0 2. Write a system of linear inequalities

### 2. Let E and F be two events of the same sample space. If P (E) =.55, P (F ) =.70, and

c Dr. Patrice Poage, August 23, 2017 1 1324 Exam 1 Review NOTE: This review in and of itself does NOT prepare you for the test. You should be doing this review in addition to all your suggested homework,

### PROBABILITY. 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

### Probability Review before Quiz. Unit 6 Day 6 Probability

Probability Review before Quiz Unit 6 Day 6 Probability Warm-up: Day 6 1. A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be

### Fair Game Review. Chapter 9. Simplify the fraction

Name Date Chapter 9 Simplify the fraction. 1. 10 12 Fair Game Review 2. 36 72 3. 14 28 4. 18 26 5. 32 48 6. 65 91 7. There are 90 students involved in the mentoring program. Of these students, 60 are girls.

### Bell Work. Warm-Up Exercises. Two six-sided dice are rolled. Find the probability of each sum or 7

Warm-Up Exercises Two six-sided dice are rolled. Find the probability of each sum. 1. 7 Bell Work 2. 5 or 7 3. You toss a coin 3 times. What is the probability of getting 3 heads? Warm-Up Notes Exercises

### 13-6 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

### Chance 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

### Math 1070 Sample Exam 1

University of Connecticut Department of Mathematics Math 1070 Sample Exam 1 Exam 1 will cover sections 4.1-4.7 and 5.1-5.4. This sample exam is intended to be used as one of several resources to help you

### 0-5 Adding Probabilities. 1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins.

1. CARNIVAL GAMES A spinner has sections of equal size. The table shows the results of several spins. d. a. Copy the table and add a column to show the experimental probability of the spinner landing on

### NOTES Unit 6 Probability Honors Math 2 1

NOTES Unit 6 Probability Honors Math 2 1 Warm-Up: Day 1: Counting Methods, Permutations & Combinations 1. Given the equation y 4 x 2draw the graph, being sure to indicate at least 3 points clearly. Solve

### Math 7 Notes - Unit 11 Probability

Math 7 Notes - Unit 11 Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare theoretical

### Unit 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

### Study Island Statistics and Probability

Study Island Statistics and Probability Copyright 2014 Edmentum - All rights reserved. 1. An experiment is broken up into two parts. In the first part of the experiment, a six-sided die is rolled. In the

### 10-4 Theoretical Probability

Problem of the Day A spinner is divided into 4 different colored sections. It is designed so that the probability of spinning red is twice the probability of spinning green, the probability of spinning

### Probability 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

### April 10, ex) Draw a tree diagram of this situation.

April 10, 2014 12-1 Fundamental Counting Principle & Multiplying Probabilities 1. Outcome - the result of a single trial. 2. Sample Space - the set of all possible outcomes 3. Independent Events - when

### Lesson 16.1 Assignment

Lesson 16.1 Assignment Name Date Rolling, Rolling, Rolling... Defining and Representing Probability 1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks. He

### Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes

NYS COMMON CORE MAEMAICS CURRICULUM 7 : Calculating Probabilities for Chance Experiments with Equally Likely Classwork Examples: heoretical Probability In a previous lesson, you saw that to find an estimate

### Exercise 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

### MULTIPLE 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

### Name: Period: Date: 7 th Pre-AP: Probability Review and Mini-Review for Exam

Name: Period: Date: 7 th Pre-AP: Probability Review and Mini-Review 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

### Independent and Mutually Exclusive Events

Independent and Mutually Exclusive Events By: OpenStaxCollege Independent and mutually exclusive do not mean the same thing. Independent Events Two events are independent if the following are true: P(A

### 10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!)

10.1 Applying the Counting Principle and Permutations (helps you count up the number of possibilities!) Example 1: Pizza You are buying a pizza. You have a choice of 3 crusts, 4 cheeses, 5 meat toppings,

### Probability and Statistics 15% of EOC

MGSE9-12.S.CP.1 1. Which of the following is true for A U B A: 2, 4, 6, 8 B: 5, 6, 7, 8, 9, 10 A. 6, 8 B. 2, 4, 6, 8 C. 2, 4, 5, 6, 6, 7, 8, 8, 9, 10 D. 2, 4, 5, 6, 7, 8, 9, 10 2. This Venn diagram shows

### 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

### LC 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

### A. 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

### Probability. The MEnTe Program Math Enrichment through Technology. Title V East Los Angeles College

Probability The MEnTe Program Math Enrichment through Technology Title V East Los Angeles College 2003 East Los Angeles College. All rights reserved. Topics Introduction Empirical Probability Theoretical

### 4.3 Rules of Probability

4.3 Rules of Probability If a probability distribution is not uniform, to find the probability of a given event, add up the probabilities of all the individual outcomes that make up the event. Example:

### Math 1101 Combinations Handout #17

Math 1101 Combinations Handout #17 1. Compute the following: (a) C(8, 4) (b) C(17, 3) (c) C(20, 5) 2. In the lottery game Megabucks, it used to be that a person chose 6 out of 36 numbers. The order of

### 6) A) both; happy B) neither; not happy C) one; happy D) one; not happy

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### Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results:

Lenarz Math 102 Practice Exam # 3 Name: 1. A 10-sided die is rolled 100 times with the following results: Outcome Frequency 1 8 2 8 3 12 4 7 5 15 8 7 8 8 13 9 9 10 12 (a) What is the experimental probability

### Math 7 Notes - Unit 7B (Chapter 11) Probability

Math 7 Notes - Unit 7B (Chapter 11) Probability Probability Syllabus Objective: (7.2)The student will determine the theoretical probability of an event. Syllabus Objective: (7.4)The student will compare

### Such a description is the basis for a probability model. Here is the basic vocabulary we use.

5.2.1 Probability Models When we toss a coin, we can t know the outcome in advance. What do we know? We are willing to say that the outcome will be either heads or tails. We believe that each of these

### Practice 9-1. Probability

Practice 9-1 Probability You spin a spinner numbered 1 through 10. Each outcome is equally likely. Find the probabilities below as a fraction, decimal, and percent. 1. P(9) 2. P(even) 3. P(number 4. P(multiple

### Mutually Exclusive Events

Mutually Exclusive Events Suppose you are rolling a six-sided die. What is the probability that you roll an odd number and you roll a 2? Can these both occur at the same time? Why or why not? Mutually

### Raise your hand if you rode a bus within the past month. Record the number of raised hands.

166 CHAPTER 3 PROBABILITY TOPICS Raise your hand if you rode a bus within the past month. Record the number of raised hands. Raise your hand if you answered "yes" to BOTH of the first two questions. Record

### ATHS FC Math Department Al Ain Remedial worksheet. Lesson 10.4 (Ellipses)

ATHS FC Math Department Al Ain Remedial worksheet Section Name ID Date Lesson Marks Lesson 10.4 (Ellipses) 10.4, 10.5, 0.4, 0.5 and 0.6 Intervention Plan Page 1 of 19 Gr 12 core c 2 = a 2 b 2 Question

### Math 1 Unit 4 Mid-Unit Review Chances of Winning

Math 1 Unit 4 Mid-Unit Review Chances of Winning Name My child studied for the Unit 4 Mid-Unit Test. I am aware that tests are worth 40% of my child s grade. Parent Signature MM1D1 a. Apply the addition

### Counting 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

### Essential Question How can you list the possible outcomes in the sample space of an experiment?

. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G..B Sample Spaces and Probability Essential Question How can you list the possible outcomes in the sample space of an experiment? The sample space of an experiment

### Probability of Independent Events. If A and B are independent events, then the probability that both A and B occur is: P(A and B) 5 P(A) p P(B)

10.5 a.1, a.5 TEKS Find Probabilities of Independent and Dependent Events Before You found probabilities of compound events. Now You will examine independent and dependent events. Why? So you can formulate

### Quiz 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

### Functional 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

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 00 -- PRACTICE EXAM 3 Millersville University, Fall 008 Ron Umble, Instr. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given question,

### Classical 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

### 2 Event is equally likely to occur or not occur. When all outcomes are equally likely, the theoretical probability that an event A will occur is:

10.3 TEKS a.1, a.4 Define and Use Probability Before You determined the number of ways an event could occur. Now You will find the likelihood that an event will occur. Why? So you can find real-life geometric

### XXII 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

### Fundamentals of Probability

Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible