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) 0.028 B) 0.033 C) 0.024 D) 0.039 1) 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) 0.007 B) 0.125 C) 0.531 D) 0.157 E) 0.029 3) 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) 0.593 B) 0.457 C) 0.231 D) 2.31 E) 0.012 4) You roll a fair die three times. What is the probability that you roll at least one 2? A) 0.005 B) 0.167 C) 0.5 D) 0.421 E) 0.579 2) 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) 0.333 C) 0.077 D) 0.5 E) 0.25 5) 6) The table below describes the smoking habits of a group of asthma sufferers. 6) Light Heavy Nonsmoker smoker smoker Total Men 395 63 79 537 Women 363 86 67 516 Total 758 149 146 1053 What is the probability that a woman is a nonsmoker? A) 0.703 B) 0.720 C) 0.345 D) 0.49 E) 0.479 7) 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) 0.333 B) 0.077 C) 0.231 D) 0.25 E) 1 7) 1
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) 0.333 B) 0.077 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) 0.333 D) 0.077 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) 0.019 B) 0.931 C) 0.081 D) 0.900 E) 0.069 8) 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) 94 160 280 534 64 69 185 22 8 26 56 180 220 375 775 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) 0.176 B) 0.921 C) 0.2 D) 0.121 E) 0.800 12) 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) 0.017 B) 0.044 C) 6.031 D) 0.013 E) 0.001 12) 2
13) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 13) 12 45 79 46 182 8 47 84 30 169 59 181 296 175 711 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) 0.434 B) 0.416 C) 0.111 D) 0.267 E) 0.256 3
14) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 14) 10 37 92 44 183 9 32 92 45 178 58 158 317 188 721 Find the probability that the person was a secretary or retired before the age of 61. A) 0.306 B) 0.092 C) 0.546 D) 0.404 E) 0.455 4
15) The following contingency table provides a joint frequency distribution for a group of retired people by career and age at retirement. 15) 12 47 92 33 184 9 32 87 45 173 60 168 312 177 717 Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk. A) 0.084 B) 0.254 C) 0.099 D) 0.300 E) 0.025 16) Compute the mean of the random variable with the given discrete probability distribution 16) x P(x) 0 0.2 10 0.2 25 0.4 30 0.2 A) 11.2 B) 18 C) 16.25 D) 126.0 17) A fair coin is tossed four times. What is the probability that the sequence of tosses is HHTT? A) 0.038 B) 0.125 C) 0.25 D) 0.0625 18) 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) 0.939 B) 0.0610 C) 0.0022 D) 0.0148 17) 18) 5
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) 0.57 20) Let A and B be events with P(A) = 0.4, P(B) = 0.9, and P(A and B) = 0.32. 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) 5 0.5 6 0.4 7 0.45 8-0.35 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 50,000 30 26 27 19 50,000-500,000 60 48 50 39 Over 500,000 72 125 79 48 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) 0.265 B) 0.255 C) 0.164 D) 0.043 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) 1.750 B) 1.625 C) 2.500 D) 1.938 E) 1.875 24) 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) $3.46 23) 24) 6
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 0 1 2 A) P(Rainy days) 0.49 0.06 0.24 Rainy days 0 1 2 B) P(Rainy days) 0.49 0.21 0.24 Rainy days 0 1 2 C) P(Rainy days) 0.49 0.42 0.09 Rainy days 0 1 2 D) P(Rainy days) 0.14 0.62 0.24 Rainy days 0 1 2 E) P(Rainy days) 0.49 0.27 0.24 25) 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) 36 12 3 1 Amount won $0 $15 $30 $80 36 12 4 1 P(Amount won) Amount won $0 $15 $30 $50 P(Amount won) 39 4 4 1 Amount won $0 $15 $30 $50 P(Amount won) 36 12 3 1 Amount won $0 $15 $30 $80 P(Amount won) 32 16 3 1 26) 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
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) 0.4000 B) 0.0634 C) 0.0000 D) 0.0016 29) 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) 0.0153 B) 0.0028 C) 0.9847 D) 0.0573 30) 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) 0.6 31) 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) $2250 32) Determine whether the table represents a discrete probability distribution. 28) 29) 30) 31) 32) x P(x) 3 0.3 4 0.05 5 0.45 6 0.2 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) = 0.45. 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) 0.5 33) 34) 8
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) 0.9959 B) 0.9816 C) 0.0184 D) 0.0041 36) 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) $3750 37) 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) 0.9757 B) 0.0243 C) 0.1845 D) 0.8155 38) Fill in the missing value so that the following table represents a probability distribution. 35) 36) 37) 38) x -2-1 0 1 P(x) 0.05 0.47? 0.32 A) 0.25 B) 0.02 C) 0.07 D) 0.16 39) Let A and B be events with P(A) = 0.2, P(B) = 0.5, and P(A and B) = 0.08. Are A and B independent? A) No B) Yes 39) 9
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