Math 3201 Midterm Chapter 3

Transcription

1 Math 3201 Midterm Chapter 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which expression correctly describes the experimental probability P(B), where n(b) is the number of times event B occurred and n(t) is the total number of trials, T, in the experiment? 2. Which expression correctly describes the theoretically probability P(X), where n(x) is the number of times event X occurred and n(s) is the number of outcomes in the sample space, S, where all outcomes are equally likely? 3. Given the following probabilities, which event is most likely to occur? P(A) = 0.2 P(B) = P(C) = 0.3 P(D) = 4. Three events, A, B, and C, are all equally likely. If there are no other possible events, which of the following statements is true? P(A) = 0 P(B) = P(C) = 1 P(A) = 3 1

2 5. 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. 4 : 7 4 : 11 7 : 11 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. 3 : 1 1 : 3 1 : 1 3 : Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the wall 7 times in 28 attempts. Determine the odds against Zahra climbing to the top. 3 : 1 4 : 1 3 : 11 3 : 4 8. 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 Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the wall 7 times in 28 attempts. Determine the probability of Zahra climbing to the top this time The weather forecaster says that there is a 50% probability of showers tomorrow. Determine the odds against showers. 1 : 1 5 : 10 2 : 1 1 : 2 2

3 11. 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. 2 P 2 2 P 1 18 P 2 18 P A credit card company randomly generates temporary four-digit pass codes for cardholders. Determine the number of four-digit pass codes 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. 18 P P 4 18 P 2 18 P Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the total number of outcomes 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 % 33.45% 39.06% 46.91% 3

4 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 multiple of Two dice are rolled. Let A represent rolling a sum greater than 10. Let B represent rolling a sum that is a multiple of 2. Determine n(a B) Helen is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a black card or a spade. 19. Brian rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 5 and the sum of the two dice is greater than 9, Brian wins a point. Determine the probability that Brian will win a point. 4

5 20. Sarah 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 NOT face cards. 21. 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. 22. Misha draws a card from a well-shuffled standard deck of 52 playing cards. Then he puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are even numbers. 5

6 23. Select the events that are dependent. Drawing a face card from a standard deck of 52 playing cards, putting it back, and then drawing another face card. Rolling a 4 and rolling a 3 with a pair of six-sided dice, numbered 1 to 6. Drawing a heart from a standard deck of 52 playing cards, putting it back, and then drawing another heart. Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered 1 to Select the events that are independent. Drawing a 10 from a standard deck of 52 playing cards and then drawing another card, without replacing the first card. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6. Choosing a number between 1 and 20 with the number being a multiple of 3 and also a multiple of 9. Drawing a diamond from a standard deck of 52 playing cards and then drawing another diamond, without replacing the first card. 25. 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 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 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 % 19.64% 26.47% 32.13% 6

7 28. 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. 1.96% 9.05% 14.32% 23.08% 29. Select the independent events. P(A) = 0.22, P(B) = 0.39, and P(A B) = P(A) = 0.18, P(B) = 0.7, and P(A B) = P(A) = 0.51, P(B) = 0.1, and P(A B) = P(A) = 0.9, P(B) = 0.23, and P(A B) = There are three children in the Jaffna family. Determine the probability that they have two boys and a girl. 12.5% 25% 37.5% 50% Short Answer 1. Josephine plays ringette. She has scored 3 times in 15 shots on goal. She says that the odds in favour of her scoring are 1 to 5. Is she right? Explain. 2. The coach of a basketball team claims that, for the next game, the odds in favour of the team winning are 7 : 3, the odds in favour of the team losing are 1 : 9, and the odds against a tie are 4 : 1. Are these odds possible? Explain. 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. 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. 5. Access to a particular online game is password protected. Every player must create a password that consists of four capital letters followed by three 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 E, J, M, and T. 7

8 6. Abigail needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that the first digit of her password will be even and the third digit will be odd. 7. 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. 8. 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 State whether the following events are mutually exclusive and explain your reasoning. Drawing a heart or drawing a Jack from a standard deck of 52 playing cards. 10. Luke is playing a board game. He must roll doubles (event A) or a sum of 6 (event B). Draw a Venn diagram to represent the two events. 11. Brittany rolls two six-sided dice, numbered 1 to 6. Determine the probability that she rolls an odd sum or a sum of The probability that Eva will go to the gym on Saturday is 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. 13. Matias rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 2 and the sum of the two dice is greater than 4, Matias wins a point. Determine, to the nearest tenth of a percent, the probability that Matias will win a point. 14. Anneliese 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, to the nearest tenth of a percent, the probability that both cards are red. 15. 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. 16. A computer manufacturer knows that, in a box of 175 computer chips, 5 will be defective. Max will draw 2 chips at random, from a box of 175. Determine, to the nearest thousandth, the probability that Max will draw 2 non-defective chips. 17. A standard red die and a four-sided green die are rolled. Determine, to the nearest hundredth of a percent, the probability of rolling a 6 on the red die and a 2 on the green die. 8

9 18. A die is rolled twice. Determine the probability that the first roll is a 3 and the second roll is a Suppose that P(A) = 0.4, P(B) = 0.2, and P(A B) = Are events A and B independent? Explain. 20. Suppose that P(A) = 0.7, P(B) = 0.34, and P(A B) = Are events A and B independent? Explain. Problem 1. A hockey game has ended in a tie after a 5 min overtime period, so the winner will be decided by a shootout. The coach must decide whether Leanne or Krysta should go first in the shootout. The coach would prefer to use her best scorer first, so she will base her decision on the players shootout records. Player Attempts Goals Scored Leanne 12 8 Krysta 14 9 Who should go first? Show your work. 2. A group of students are holding a charity carnival to support a local animal shelter. The students have created a dice game that they call Zim and a card game that they call Bap. The odds against winning Zim are 3 : 1, and the odds against winning Bap are 4 : 5. Which game should Sarah play? Show your work. 3. A group of students are holding a charity carnival to support a local animal shelter. The students have created a dice game that they call Boing and a card game that they call Zoop. The odds against winning Boing are 9 : 5, and the odds against winning Zoop are 7 : 2. Which game should Sylvia play? Show your work. 4. A high-school football team has the ball at the opponent s 2 yd line. It is the third down. The team is behind by 3 points, with only one second left in the game. The players have two options: They can try to score a touchdown. In the past, they have succeeded 8 out of 14 times. If they score a touchdown, they will win the game. They can try to kick a field goal. The kicker has scored a field goal from 20 yd or less in 3 out of 5 tries. If they score a field goal, they will get 3 points and tie the game forcing overtime. a) What are the odds in favour of each option? Show your work. b) Which option should the coach choose? Explain. 5. 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? 9

10 6. Homer hosts a morning radio show in Halifax. To advertise his show, he is holding a contest at a local mall. He spells out NOVA SCOTIA with letter tiles. Then he turns the tiles face down and mixes them up. He asks Marie to arrange the tiles in a row and turn them face up. If the row of tiles spells NOVA SCOTIA, Marie will win a new car. Determine the probability that Marie will win the car. Show your work. 7. There are 20 bikes in a spinning class. The bikes are arranged in 4 rows, with 5 bikes in each row. They hope to be in the same row, but they cannot request a specific bike. Determine the probability that all 5 friends will be in the same row, with Jeff and Dariya at either end. Show your work. 8. Each day, Julia s math teacher gives the class a warm-up question. It is a true-false question 20% of the time and a multiple-choice question 80% of the time. Julia gets 70% of the true-false questions correct, and 90% of the multiple-choice questions correct. Julia answers today s question correctly. What is the probability that it was a multiple-choice question? Show your work. 9. Trista remembers to set her alarm clock 82% of the time. When she does remember to set her alarm clock, the probability that she will be late for school is When she does not remember to set it, the probability that she will be late for school is Trista was late today. What is the probability that she remembered to set her alarm clock? Show your work. 10. Elin estimates that her probability of passing French is 0.6 and her probability of passing chemistry is 0.8. Determine the probability that Elin will pass French but fail chemistry. Show your work. 10