Review Sheet: Chapter 3 - Probability

[Pages:9]Review Sheet: Chapter 3 - Probability

____ 1. Given the following probabilities, which event is most likely to occur?

A. P(A) = 0.28 B.

P(B) = C. P(C) = 0.27 D.

P(D) =

____ ____ ____ ____ ____ ____ ____

2. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls out a coin at random. Determine the odds against the coin being a quarter.

A. 1 : 4 B. 1 : 3 C. 3 : 4 D. 3 : 1

3. Julie draws a card at random from a standard deck of 52 playing cards. Determine the odds in favour of the card being a heart.

A. 3 : 1 B. 1 : 3 C. 1 : 1 D. 3 : 13

4. Tia notices that yogurt is on sale at a local grocery store. The last eight times that yogurt was on sale, it was available only three times. Determine the odds against yogurt being available this time.

A. 3 : 5 B. 3 : 8 C. 5 : 8 D. 5 : 3

5. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls out a coin at random. Determine the probability of the coin being a quarter.

A. 0.250 B. 0.333 C. 0.750 D. 0.848

6. Julie draws a card at random from a standard deck of 52 playing cards. Determine the probability of the card being a diamond.

A. 0.250 B. 0.500 C. 0.625 D. 0.750

7. The weather forecaster says that there is a 30% probability of fog tomorrow. Determine the odds against fog.

A. 3 : 7 B. 3 : 10 C. 7 : 3 D. 7 : 10

8. A sports forecaster says that there is a 40% probability of a team winning their next game. Determine the odds against that team winning their next game.

A. 2 : 3 B. 2 : 5 C. 3 : 5 D. 3 : 2

____

9. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary. Determine the number of ways in which these 2 people can be chosen for president and secretary.

____

A. 2P2 B. 2P1 C. 18P2 D. 18P16

10. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary. Determine the total number of possible committees.

____

A. 18P16 B. 18P4 C. 18P2 D. 18P12

11. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the probability that there will be equal numbers of boys and girls on the trip.

A. 17.23% B. 22.61% C. 27.35% D. 34.06%

____ 12. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the number of ways in which there can be more girls than boys on the trip.

A. 17 456 B. 25 872 C. 29 778 D. 35 910

____ 13. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the van. Determine the probability that only boys will be sitting at the front.

A. 28.57% B. 33.45% C. 39.06% D. 46.91%

____ 14. Yvonne tosses three coins. Determine the probability that at least one coin will land as heads.

A. 12.5% B. 37.5% C. 62.5% D. 87.5%

____ 15. Two dice are rolled. Let A represent rolling a sum greater than 7. Let B represent rolling a sum that is a multiple of 3. Determine n(A B).

A. 5 B. 8 C. 12 D. 15

____ 16. Select the events that are mutually exclusive.

A. Drawing a 7 or drawing a heart from a standard deck of 52 playing cards. B. Rolling a sum of 4 or rolling an even number with a pair of four-sided dice, numbered 1 to

4. C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards. D. Rolling a sum of 8 or a sum of 11 with a pair of six-sided dice, numbered 1 to 6.

____ 17. Roena is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a heart or a King. A. B. C. D.

____ 18. Hilary draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine the probability that both cards are hearts. A. B. C. D.

____

19. Min draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are face cards.

A.

B.

C.

D.

____

20. Select the events that are dependent. A. Rolling a 2 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6. B. Drawing an odd card from a standard deck of 52 playing cards, putting it back, and then drawing another odd card. C. Drawing a spade from a standard deck of 52 playing cards and then drawing another spade, without replacing the first card. D. Rolling an even number and rolling an odd number with a pair of six-sided dice, numbered 1 to 6.

____

21. Select the events that are independent. A. Drawing a 10 from a standard deck of 52 playing cards and then drawing another card, without replacing the first card. B. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6. C. Choosing a number between 1 and 20 with the number being a multiple of 3 and also a multiple of 9. D. Drawing a diamond from a standard deck of 52 playing cards and then drawing another diamond, without replacing the first card.

____

22. There are 60 males and 90 females in a graduating class. Of these students, 30 males and 50 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.

A. 0.41 B. 0.47 C. 0.53 D. 0.59

____

23. Paul has four loonies, three toonies, and five quarters in his pocket. He needs two quarters for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are quarters.

A. 15.15% B. 19.64% C. 26.47% D. 32.13%

____ 24. A four-sided red die and a six-sided green die are rolled. Determine the probability of rolling a 2 on the red die and a 5 on the green die.

A. 4.17% B. 4.89% C. 6.50% D. 8.04%

____ 25. Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the probability of drawing a face card then drawing an even-numbered card.

A. 1.96% B. 9.05% C. 14.32% D. 23.08%

____ 26. Select the independent events.

A. P(A) = 0.67, P(B) = 0.12, and P(A B) = 0.086 B. P(A) = 0.83, P(B) = 0.4, and P(A B) = 0.378 C. P(A) = 0.4, P(B) = 0.91, and P(A B) = 0.364 D. P(A) = 0.2, P(B) = 0.32, and P(A B) = 0.046

Short Answer

1. A credit card company randomly generates temporary five-digit pass codes for cardholders. Meghan is expecting her credit card to arrive in the mail. Determine, to the nearest hundredth of a percent, the probability that her pass code will consist of five different even digits.

2. From a committee of 12 people, 3 of these people are randomly chosen to be president, vice-president, and secretary. Determine, to the nearest hundredth of a percent, the probability that Pavel, Rashida, and Jerry will be chosen.

3. Access to a particular online game is password protected. Every player must create a password that consists of three capital letters followed by two digits. Repetitions are NOT allowed in a password. Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters J, K, and L.

4. Ashley has letter tiles that spell NAPKIN. She has selected three of these tiles at random. Determine the probability that the tiles she selected are two consonants and one vowel.

Problem

1. Three people are running for president of the student council. The polls show Denis has a 55% chance of winning, Cyndi has a 25% chance of winning, and Chris has a 20% chance of winning. a) What are the odds in favour of each person winning? Show your work. b) Suppose that Chris withdraws and offers his support to Cyndi. Further suppose that his supporters also switch to Cyndi. What are the odds in favour of Cyndi winning now?

2. Atian, Sam, Phuong, Mike, and Tariq are competing with ten other boys to be on their school's cross-country team. All the boys have an equal chance of winning the trial race. Determine the probability that Atian, Sam, Phuong, Mike, and Tariq will place first, second, third, fourth, and fifth, in any order. Show your work.

3. A student council consists of 12 girls and 8 boys. To form a subcommittee, 4 students are randomly selected from the council. Determine the odds in favour of 3 girls and 1 boy being on the subcommittee. Show your work.

4. A car manufacturer keeps a database of all the cars that are available for sale at all the dealerships in Western Canada. For model A, the database reports that 36% have heated leather seats, 41% have a sunroof, and 52% have neither. Determine the probability of a model A car at a dealership having both heated leather seats and a sunroof. Show your work.

5. A survey reported that 29% of households have one or more dogs, 35% have one or more cats, and 42% have neither dogs nor cats. Suppose that a household is selected at random. Determine the probability that there are cats but no dogs in the household. Show your work.

6. Aisha plays the balloon pop game at a carnival. There are 50 balloons, with the name of a prize inside each balloon. The prizes are 10 stuffed bears, 6 toy trucks, 21 decks of cards, 9 yo-yos, and 4 giant stuffed dogs. Aisha pops a balloon with a dart. Determine the odds in favour of her winning either a stuffed dog or a stuffed bear. Show your work.

7. On Tuesday, the weather forecaster says that there is a 40% chance of snow on Wednesday and a 50% chance of snow on Thursday. The forecaster also says that there is a 10% chance of snow on both Wednesday and Thursday. Determine the probability that there will be snow on Wednesday or on Thursday. Show your work.

8. A jar contains 8 green marbles and some green marbles. The odds against selecting a randomly chosen red marble are 1:5. Show all workings to determine A) how many green marbles are in the jar B)total number of marbles in the jar.

9. A 6 digit number is generated from the following digits 3, 2, 7, 9, 6, 5 with no repetition. Find the probability of the number that is formed that is will be:

A) An odd number B) An even number C) The odds against an even number being formed

10. There are 13 teachers and 5 administrators at a conference.

A) Find the number of ways you can award 3 prizes to teachers only. B) Find the number ways to give out the four prizes to all people at the conference? C) Find the probability that all of the 3 prizes went to teachers? To Administrators?

11. A jar contains 5 red, 8 blue and 10 purple candies. If the total number of candies is 30, find the probability that a handful of 4 contains one of each type?

12. Mark, Nancy, Olivia, Paul, Quinlan, Victor, and Roxy are standing in a line.

A) Determine the total possible arrangements. B) Determine how many ways Quinlan and Roxy could be standing together. Use this to determine

the probability Mark and Nancy will be standing together? What are odds this will NOT be standing together? C) What is the probability that Paul and Quinlan are NOT standing together?

13. In a class survey, 61% play sports, 37% play a musical instrument, 19% play neither. Draw a Venn diagram to illustrate whether the events are mutually exclusive or non-mutually exclusive. Use it to determine

A) the probability someone play a musical instrument or plays sports B) the probability someone does not play a musical instrument C) the probability someone plays a sport only

14. A person is being selected to draw a marble from a bag. The odds of selecting a male from the group are 7:10 while the odds of selecting a green marble are 1: 4. What is the PROABILITY of a non-green marble being selecting by a female in the group? (AND is implied YES or NO?)

Review Sheet Answer Section

MULTIPLE CHOICE

1. ANS: A 2. ANS: B 3. ANS: B 4. ANS: D 5. ANS: C 6. ANS: A 7. ANS: C 8. ANS: D 9. ANS: A 10. ANS: C 11. ANS: D 12. ANS: B 13. ANS: A 14. ANS: D 15. ANS: A 16. ANS: D 17. ANS: A 18. ANS: B 19. ANS: B 20. ANS: C 21. ANS: B 22. ANS: A 23. ANS: A 24. ANS: A 25. ANS: B 26. ANS: C

SHORT ANSWER 1. ANS: 0.12%

2. ANS: 0.45%

3. ANS: 0.038%

4. ANS: 60%

PROBLEM

1. ANS: a) The odds in favour of Denis winning are 55 : (100 ? 55). This is equal to 55: 45 or 11 : 9. The odds in favour of Cyndi winning are 25 : (100 ? 25). This is equal to 25 : 75 or 1 : 3. The odds in favour of Chris winning are 20 : (100 ? 20). This is equal to 20 : 80 or 1 : 4. b) If Chris' 20% support goes to Cyndi, then her support will now be 45%, and the odds in favour of Cyndi winning will be the same as the odds against Denis winning. So, the odds in favour of Cyndi winning are 45 : 55 or 9 : 11.

2. ANS: Atian, Sam, Phuong, Mike, and Tariq can place first, second, third, fourth, or fifth, in any order. There are 5! or 120 ways in which five runners can place in five positions. There are 15P5 ways that 15 runners can place first, second, third, fourth, or fifth.

There are 360 360 possible outcomes. P(A, S, P, M, and T place 1, 2, 3, 4, or 5) =

P(A, S, P, M, and T place 1, 2, 3, 4, or 5) =

or

The probability that Atian, Sam, Phuong, Mike, and Tariq will place in the top five positions is

or about 0.03%.

3. ANS: Let T represent three girls and one boy being chosen to form a subcommittee, and let S represent all possible subcommittees. In this example, order is not important. The number of ways to arrange three girls and one boy from 12 girls and 8 boys is 12C3 8C1.

The number of ways to arrange 20 people in a four-person committee is 20C4.

The probability can now be determined:

The odds in favour that the committee will contain 3 girls and 1 boy is 352 : (969 ? 352) or 352 : 617. 4. ANS: Let A represent the universal set of all model A cars. Let L represent model A cars with heated leather seats. Let S represent model A cars with a sunroof. P(L S) = 100% ? 52% P(L S) = 48%

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