MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The letters "A", "B", "C", "D", "E", and "F" are written on six slips of paper, and the slips are placed into a hat. If the slips are drawn randomly without replacement, what is the probability that "A" is drawn first and "B" is drawn second? A) B) C) D) ) Solve the problem. Round your answer, as needed. 2) There is a huge pile of buttons in which 29% are black, 11% are blue, 17% are orange, 24% are white, and the rest are clear. You close your eyes, choose a button at random, write down what color it is, and then put it back in the pile. What is the probability that the third button you choose is the first one thatʹs clear? A) B) C) D) E) ) A manufacturing process has a 77% yield, meaning that 77% of the products are acceptable and 23% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. A) B) C) D) 2.31 E) ) You roll a fair die three times. What is the probability that you roll at least one 2? A) B) C) 0.5 D) E) ) 3) 4) Find the indicated probability. 5) You draw a card at random from a standard deck of cards. Find the probability that the card is a spade given that it is not a diamond. A) 0 B) C) D) 0.5 E) ) 6) The table below describes the smoking habits of a group of asthma sufferers. 6) Light Heavy Nonsmoker smoker smoker Total Men Women Total What is the probability that a woman is a nonsmoker? A) B) C) D) 0.49 E) ) You draw a card at random from a standard deck of cards. Find the probability that the card is a face card given that it is a king. A) B) C) D) 0.25 E) 1 7) 1
2 8) You draw a card at random from a standard deck of cards. Find the probability that the card is a heart given that it is black. A) B) C) 0 D) 0.25 E) 0.5 9) You draw a card at random from a standard deck of cards. Find the probability that the card is a diamond given that it is a queen. A) 0.5 B) 0.25 C) D) E) 0 10) A box contains 16 batteries of which 7 are still working. Anne starts picking batteries one at a time from the box and testing them. Find the probability that at least one of the first four works. A) B) C) D) E) ) 9) 10) 11) An auto insurance company was interested in investigating accident rates for drivers in different age groups. The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years. 11) If one of these drivers is selected at random, find the probability that the person has had no accidents in the last three years or is younger than 25. A) B) C) 0.2 D) E) ) A box contains 12 batteries of which 5 are still working. Anne starts picking batteries one at a time from the box and testing them. Find the probability that she has to pick 5 batteries in order to find one that works. A) B) C) D) E) ) 2
3 13) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 13) Suppose one of these people is selected at random. Compute the probability that the person selected was an attorney who retired between 61 and 65. A) B) C) D) E)
4 14) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 14) Find the probability that the person was a secretary or retired before the age of 61. A) B) C) D) E)
5 15) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 15) Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk. A) B) C) D) E) ) Compute the mean of the random variable with the given discrete probability distribution 16) x P(x) A) 11.2 B) 18 C) D) ) A fair coin is tossed four times. What is the probability that the sequence of tosses is HHTT? A) B) C) 0.25 D) ) It is estimated that 45% of households own a riding lawn mower. A sample of 11 households is studied. What is the probability that more than 8 of these own a riding lawn mower? A) B) C) D) ) 18) 5
6 19) Let A and B be events with P(A) = 0.7, P(B) = 0.5, and P(B A) = 0.4. Find P(A and B). A) 0.28 B) 0.35 C) 0.2 D) ) Let A and B be events with P(A) = 0.4, P(B) = 0.9, and P(A and B) = Are A and B mutually exclusive? A) No B) Yes 21) Determine whether the table represents a discrete probability distribution. 19) 20) 21) x P(x) A) No B) Yes 22) A fast-food restaurant chain has 623 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 623 to test market a new menu. 22) Region Population of city NE SE SW NW Under 50, , , Over 500, Given that the outlet is located in a city with a population under 50,000, what is the probability that it is in the Southwest? A) B) C) D) Find the expected value of the random variable. 23) A couple plans to have children until they get a boy, but they agree that they will not have more than four children even if all are girls. Find the expected number of children they will have. Assume that boys and girls are equally likely. Round your answer to three decimal places. A) B) C) D) E) ) You pick a card from a deck. If you get a face card, you win $10. If you get an ace, you win $25 plus an extra $40 for the ace of hearts. For any other card you win nothing. Find the expected amount you will win. A) $5.00 B) $5.77 C) $5.48 D) $4. E) $ ) 24) 6
7 Create a probability model for the random variable. 25) You have arranged to go camping for two days in March. You believe that the probability that it will rain on the first day is 0.3. If it rains on the first day, the probability that it also rains on the second day is 0.8. If it doesnʹt rain on the first day, the probability that it rains on the second day is 0.3. Let the random variable X be the number of rainy days during your camping trip. Find the probability model for X. Rainy days A) P(Rainy days) Rainy days B) P(Rainy days) Rainy days C) P(Rainy days) Rainy days D) P(Rainy days) Rainy days E) P(Rainy days) ) 26) You pick a card from a deck. If you get a face card, you win $15. If you get an ace, you win $30 plus an extra $50 for the ace of hearts. For any other card you win nothing. Create a probability model for the amount you win at this game. Amount won $0 $15 $30 $80 A) B) C) D) E) P(Amount won) Amount won $0 $15 $30 $ P(Amount won) Amount won $0 $15 $30 $50 P(Amount won) Amount won $0 $15 $30 $50 P(Amount won) Amount won $0 $15 $30 $80 P(Amount won) ) 27) Assume a soldier is selected at random from the Army. Determine whether the events A and B are independent, mutually exclusive, or neither. 27) A: The soldier is a corporal. B: The soldier is a colonel. A) independent B) mutually exclusive C) neither 7
8 28) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 15, p = 0.4, P(12) A) B) C) D) ) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 12, p = 0.6, P(Fewer than 4) A) B) C) D) ) Let A and B be events with P(A) = 0.8, P(B) = 0.6. Assume that A and B are independent. Find P(A and B). A) 0.8 B) 0.48 C) 0.75 D) ) An investor is considering a $15,000 investment in a start-up company. She estimates that she has probability 0.15 of a $5000 loss, probability 0.15 of a $10,000 loss, probability 0.15 of a $30,000 profit, and probability 0.55 of breaking even (a profit of $0). What is the expected value of the profit? A) $10,500 B) $6750 C) $5000 D) $ ) Determine whether the table represents a discrete probability distribution. 28) 29) 30) 31) 32) x P(x) A) No B) Yes 33) Let A and B be events with P(A) = 0.9, P(B) = 0.5, and P(A and B) = Are A and B independent? A) No B) Yes 34) An unfair coin has a probability 0.4 of landing heads. The coin is tossed two times. What is the probability that it lands heads at least once? A) 0.64 B) 0.84 C) 0.6 D) ) 34) 8
9 35) It is estimated that 45% of households own a riding lawn mower. A sample of 17 households is studied. What is the probability that no more than 3 of these own a riding lawn mower? A) B) C) D) ) An investor is considering a $10,000 investment in a start-up company. She estimates that she has probability 0.15 of a $5000 loss, probability 0.1 of a $15,000 profit, probability 0.2 of a $15,000 profit, and probability 0.55 of breaking even (a profit of $0). What is the expected value of the profit? A) $50 B) $8333 C) $9250 D) $ ) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 13 adult dogs is studied. What is the probability that exactly 9 of them weigh 65 lb or more? A) B) C) D) ) Fill in the missing value so that the following table represents a probability distribution. 35) 36) 37) 38) x P(x) ? 0.32 A) 0.25 B) 0.02 C) 0.07 D) ) Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = Are A and B independent? A) No B) Yes 39) 9
10 Answer Key Testname: UNTITLED1 1) B 2) B 3) B 4) D 5) B 6) A 7) E 8) C 9) B 10) B 11) E 12) B 13) C 14) E 15) B 16) B 17) D 18) D 19) A 20) A 21) A 22) A 23) E 24) A 25) E 26) A 27) B 28) D 29) A 30) B 31) D 32) B 33) B 34) A 35) C 36) D 37) B 38) D 39) A 10
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