Math 3201 Chapter 3 Final Review - Mr. White's course site

Math 3201

Chapter 3

Multiple Choice Identify the choice that best completes the statement or answers the question.

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

A. P(A) = 0.2 B. P(B) =

C. P(C) = 0.3 D. P(D) =

Final Review

____ ____

2. Three events, A, B, and C, are all equally likely. If there are no other possible events, which of the following statements is true?

A. P(A) = 0 B. P(B) =

C. P(C) = 1 D. P(A) = 3

3. The odds in favour of Macy passing her driver's test on the first try are 7 : 4. Determine the odds against Macy passing her driver's test on the first try.

____ ____ ____

A. 4 : 7 B. 4 : 11 C. 7 : 11 D. 3 : 11

4. 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

5. The odds in favour of Macy passing her driver's test on the first try are 7 : 4. Determine the probability that she will pass her driver's test.

A. 0.226 B. 0.364 C. 0.571 D. 0.636

6. 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 probability of yogurt being available this time.

____

A. 0.220 B. 0.375 C. 0.460 D. 0.625

7. The weather forecaster says that there is an 80% probability of rain tomorrow. Determine the odds against rain.

A. 4 : 5 B. 4 : 1 C. 1 : 5 D. 1 : 4

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Final Review

____ 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. A credit card company randomly generates temporary three-digit pass codes for cardholders. The pass code will consist of three different even digits. Determine the total number of pass codes using three different even digits.

____

A. 5P5 B. 5P3 C. 5P4 D. 5P1

10. 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

11. Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the number of options where at least one coin lands as heads.

A. 1 B. 3 C. 5 D. 7

____ 12. A credit card company randomly generates temporary four-digit pass codes for cardholders. Determine the number of four-digit pass codes.

A. 10 B. 100 C. 1000 D. 10 000

____ 13. 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 only boys will be on the trip.

A. 0.02% B. 0.08% C. 0.15% D. 0.23%

____ 14. 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

____ 15. 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%

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Chapter 3

Final Review

____ 16. Jake and Agnes are playing a board game. If a player rolls a sum greater than 9 or a multiple of 6, the player gets a bonus of 50 points. Determine the probability of rolling a sum greater than 9. A. B. C. D.

____ 17. Two dice are rolled. Let A represent rolling a sum greater than 6. Let B represent rolling a sum that is a multiple of 4. Determine P(A B). A. B. C. D.

____ 18. Select the events that are mutually exclusive.

A. Drawing a red card or drawing a diamond from a standard deck of 52 playing cards.

B. Rolling a sum of 8 or rolling an even number with a pair of six-sided dice, numbered 1 to 6.

C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards.

D. Drawing a 3 or drawing an even card from a standard deck of 52 playing cards.

____ 19. 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.

____ 20. Select the events that are independent.

A. Choosing a number between 1 and 30 with the number being a multiple of 2 and also a multiple of 4.

B. Drawing a heart from a standard deck of 52 playing cards and then drawing another heart, without replacing the first card.

C. Rolling a 2 and having a sum greater than 4 with a pair of six-sided dice, numbered 1 to 6.

D. Rolling a 1 and rolling a 6 with a pair of six-sided dice, numbered 1 to 6.

____ 21. There are 40 males and 60 females in a graduating class. Of these students, 10 males and 20 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.

A. 0.3 B. 0.4 C. 0.5 D. 0.6

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Final Review

____ 22. Rino has six loonies, four toonies, and two quarters in his pocket. He needs two loonies for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are loonies.

A. 16.3% B. 18.4% C. 22.7% D. 25.9%

____ 23. Carlo goes to the gym and does two different cardio workouts each day. His choices include using a treadmill, a stationary bike, and running the track. Determine the probability that the next time Carlo goes to the gym will use the stationary bike and then run the track.

A. 16.7% B. 26.1% C. 33.4% D. 41.9%

____ 24. There are 20 cards, numbered 1 to 20, in a box. Two cards are drawn, one at a time, with replacement. Determine the probability of drawing an even number then drawing a number that is a multiple of 4.

A. 8.8% B. 9.3% C. 10.7% D. 12.5%

____ 25. There are three children in the Jaffna family. Determine the probability that they have two boys and a girl.

A. 12.5% B. 25% C. 37.5% D. 50%

Short Answer

1. Three events, A, B, C, D, and E, are all equally likely. If there are no other possible events, what is the probability of event B?

2. A game has three possible outcomes: A, B, and C. If P(A) = 0.6 and P(B) = 0.2, what is the probability of event C?

3. Jessica rolls a standard die. Determine the probability of her rolling a 2.

4. Ned plays hockey. He has scored 5 times out of 25 shots on goal. He says the odds in favour of him scoring are 1 : 5. Is he right? Explain.

5. Jeff has been awarded a penalty shot in a hockey game. Braden is the goalie. Jeff has scored 6 times in his last 10 penalty shots. Braden has blocked 5 of the last 10 penalty shots. Determine the odds in favour of Jeff scoring, using his data.

6. The coach of a basketball team claims that, for the next game, the odds in favour of the team winning are 5 : 3, the odds in favour of the team losing are 1 : 3, and the odds against a tie are 7 : 1. Are these odds possible? Explain.

7. A credit card company randomly generates temporary four-digit pass codes for cardholders. Serena is expecting her credit card to arrive in the mail. Determine the probability that her pass code will consist of four different odd digits.

8. 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.

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9. From a committee of 18 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 Evan, Elise, and Jaime will be chosen.

10. 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.

11. 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 allowed in a password. Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters A, D, and T.

12. 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.

13. Sonja has letter tiles that spell MICROWAVE. She has selected four of these tiles at random. Determine, to the nearest tenth of a percent, the probability that the tiles she selected are two consonants and two vowels.

14. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10 balls, numbered 1 to 10.

15. State whether the following events are mutually exclusive and explain your reasoning. Rolling a sum of 5 or a sum of 9 with a pair of six-sided dice, numbered 1 to 6.

16. Brent is playing a board game. He must roll two four-sided dice, numbered 1 to 4. Determine the probability that Brent will roll a sum of 5 or 6.

17. The probability that Eva will go to the gym on Saturday is 0.63. The probability that she will go shopping on Saturday is 0.5. The probability that she will do neither is 0.3. Determine the probability that Eva will do at least one of these activities on Saturday.

18. The probability that Randy will study on Friday night is 0.3. The probability that he will play video games on Friday night is 0.7. The probability that he will do at least one of these activities is 0.9. Determine the probability that he will do both activities.

19. The probability that Haley will exercise on Sunday is 0.6. The probability that she will go shopping on Sunday is 0.5. The probability that she will do both is 0.3. Determine the probability that Haley will do at least one of these activities on Sunday.

20. The probability that Vince will study on Friday night is 0.6. The probability that he will go out for dinner is 0.8. The probability that he will do at least one of these activities is 0.8. Determine the probability that he will do both activities.

21. A regular six-sided red die and a regular six-sided black die are rolled. The red die lands on 3 and the sum of the two dice is greater than 8. Are the two events dependent or independent?

22. A heart is drawn from a well-shuffled standard deck of 52 playing cards. Another card is drawn from the deck without replacing the first card. Are the two events dependent or independent?

23. Leslie has four identical black socks and six identical white socks loose in her drawer. She pulls out one sock at random and then another sock, without replacing the first sock. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of black socks.

24. Janelle has eight identical black socks and two identical white socks loose in her drawer. She pulls out one sock at random and then another sock, without replacing the first sock. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of white socks.

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