2. The figure shows the face of a spinner. The numbers are all equally likely to occur.

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1 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, the child wins a prize. After each turn, the marble is replaced. Casey has drawn six red marbles in a row. Which statement is true? A. If Casey selects another red marble, then 2 of her next 3 picks will be blue marbles because 2 blue marbles are selected for every 8 red marbles selected. B. The probability that Casey selects a blue marble on the next turn is higher than it was on her last turn because she has chosen so many red marbles in a row. C. The probability that Casey selects a blue marble on her next turn is the same as it was on the last turn because selections are independent of each other. D. If Casey draws 4 more times, she will select 2 blue marbles because the probability that a blue marble will be selected is 2 out of every 10 turns. 2. The figure shows the face of a spinner. The numbers are all equally likely to occur. 2. What is the probability that the pointer will land on an odd number first, then on an even number twice? page 1

2 3. Use the following information to fill in the Venn diagram below. Include more than one number in each section. Use only the first 5 numbers in each set. 3. Set X = {even numbers} Set Y = {multiples of 3} Set Z = {multiples of 5} Describe the intersection of two sets and the intersection of all three sets. 4. Which of the following are mutually exclusive events when a pair of dice is rolled? 4. I. the sum of the numbers rolled is either 7 or 11 II. the sum of the numbers rolled is either an even number or a multiple of 3 III. the sum of the numbers rolled is a prime number or an even number 5. Consider the following sets: 5. A = {2, 4, 6, 8,...} B = {3, 6, 9, 12,...} C = {5, 10, 15, 20,...} List the first 5 elements in the following set: a) A B b) A B 6. An experiment consists of selecting three people at random and noting whether each is male (M) or female (F). 6. a) What is an appropriate sample space for this experiment? b) List the event exactly one person was female. 7. Find the number of permutations. 7. 7P 3 Probability page 2 MYP IB Review 9

3 8. Mr. Bradley drew Circle A and wrote in it all the positive even numbers through 10. He drew Circle B and wrote in it all the positive multiples of 5 from 0 through Mr. Bradley wants to determine the intersection of the circles, that is, only the numbers found in both Circle A and Circle B. Which of these represents the intersection of the two circles? 9. How many different ways can you play your five favorite songs? Twenty-one students at a school have an allergy to peanuts, shellfish, or both. 10. Fourteen students at the school are allergic to peanuts. Twelve students at the school are allergic to shellfish. How many of the students are allergic to both peanuts and shellfish? 11. If P(A) = 0.3, P(B) = 0.7, and P(A B) = 0.2, what is P(B A)? One hundred employees in the restaurant business were asked if they favored a ban on styrofoam containers. The results of the survey are shown in the table. 12. Gender Favor Oppose No Opinion Males Females If an employee favors the ban, what is the probability that the employee is female? 13. Answer always, sometimes or never true: 13. Raquel and Rowena each roll a die. Raquel rolls first, then Rowena. Rowena wants to roll the same number as Raquel. These two events are independent events. Probability page 3 MYP IB Review 9

4 14. A survey of 200 students involved 80 girls and 120 boys. The number of students playing basketball and volleyball is shown in the following table: 14. Basketball Volleyball Total Boys Girls Total A student is picked at random. What is the probability that the student is a girl or plays basketball? 15. How many different 6 person volleyball teams can be formed from the 30 students in the gym class? Events M and N have probabilities such that P(M) = 0.4, P(N) = 0.28, P(M N) = 0.56, and P(M N) = Are event M and event N independent? 16. A. no, because P(M) P(N) = P(M N) B. no, because P(M) P(N) P(M N) C. yes, because P(M) + P(N) = P(M N) D. yes, because P(M) P(N) P(M N) 17. If P(A) = 0.3, P(B) = 0.7, and P(A B) = 0.2, what is P(A B)? How many different outfits can Joan make from 6 pairs of pants, 3 shirts, and 2 pairs of socks? Explain A box contains five green marbles, four silver marbles, and three black marbles. If one marble is drawn at random, determine P(green not black) Attached earlobes are correlated with the presence of a widow s peak. 350 people are randomly selected and studied. The results are: 20. What would you expect to be the value of P(attached earlobes and widow s peak) if attached earlobes and the presence of a widow s peak were independent? 21. The union of two sets is best associated with the word. 21. Probability page 4 MYP IB Review 9

5 22. If P(A B) = P(A), state the relationship between events A and B Determine which of the following represent two independent events. 23. I. P(A) = (0.7), P(B) = (0.6), P(A B) = 0.42 II. P(A) = (0.6), P(B) = (0.8), P(A B) = 0.48 III. P(A) = 0.4, P(B) = 0.6, P(A B) = 0.76 A. I only B. II only C. I and II only D. I and III only 24. Answer always, sometimes or never true: 24. A card is drawn from a marked deck with half the cards missing. A two-headed coin is then tossed. These two events are independent events. 25. The table shows the student population of Richmond High School this year. 25. Girls (G) Boys (B) Total Grade 11 (J) Grade 12 (S) Total What is P(G J)? 26. If P(A B) P(A), state the relationship between events A and B A group of people are asked about their music preferences. The number of people who say they like rock music is 283. The number who say they like country is 189. The number who say they like both types of music is 112. State the number of people who like rock OR country music In a particular math unit there were 19 techniques used in the various vector problems and 12 techniques used in the trigonometry problems. 9 of these techniques were used in both types of problems. If a student is determined to learn all of the techniques covered in the unit, how many techniques must they learn? If A and B are mutually exclusive events, then: Consider the following set of numbers: 30. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} What is the probability of drawing an odd number or a multiple of 3? 31. Evaluate: 9C Probability page 5 MYP IB Review 9

6 32. If you roll a regular 6-sided die, what is the probability of rolling an odd number or a multiple of 3? Which statement is correct about the diagram? 33. A. Set A and Set B have common members. B. Some members of Set A are members of set C. C. Some members are common to Sets A, B, and C. D. Set B has the same common members with Set A and Set C For the tree diagram, which of the following are true? I. P(C A) = 0.3 II. P(A C) = P(A)P(C) III. A and C are independent 35. Evaluate: 9C There are 7 boys and 3 girls on the New York City track team. Four runners will be selected to represent the team in the finals. 36. a) How many 4-person groups can be formed? b) How many ways can 2 boys and 2 girls be chosen? 37. The intersection of two sets is best associated with the word A combination lock can use the digits 0, 1, 2, 3, 4, 5, and 6. Assuming you cannot repeat any digits, how many 5-digit codes are possible with this lock? Show your calculations. 38. Probability page 6 MYP IB Review 9

7 39. Answer always, sometimes or never true: 39. An experiment consists of two tasks. First, a fair coin is flipped and the result is recorded. Next, a card is selected form a deck of cards and the value on the face-up side is recorded. If A represents the event a tail results for the first task and B represents the event a red card is recorded for the second task, then A and B are dependent events. 40. A card is drawn at random from a standard 52-card deck. Find the probability it is a king or black card. 40. Probability page 7 MYP IB Review 9

8 Problem-Attic format version c EducAide Software Licensed for use by Terms of Use at Probability MYP IB Review 9 12/14/ C S.CP [task] I only S.CP.5 5. {2, 3, 4, 6, 8}, {6, 12, 18, 24, 30}, {5, 6, 10, 12, 15}, {10, 15, 20, 30, 40} S.CP (MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF); (MMF, MFM, FMM) 120 ways S.CP S.CP S.CP always S.CP S.CP ,775 teams S.CP.9 B S.CP outfits S.CP S.CP ( ) ( ) = 0.33 S.CP or they are independent events S.CP.3 D S.CP.2 always S.CP S.CP they are dependent events S.CP.3

9 Teacher s Key Page P(A B) = P(A) + P(B) S.CP S.CP S.CP S.CP A I, II and III S.CP S.CP ; 63; 210 ; 1 S.CP and 38. 2,520; or 7! 2! S.CP never S.CP S.CP.7

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