#5 Modules 4-1 to 4-3

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Modules 4-1 to 4-3: Chapters 11 and 12 Question 1: Suppose we roll two fair six-sided dice. What is the probability that the sum of two numbers is seven? (a) 11/36 (b) 12/36 (c) 13/36 (d) 1/6 (e) 1/3

Question 2: A sample of size 2 is drawn at random and with replacement from the set {1, 2, 3, 4, 5}. What is the probability that the sum of two numbers is an even number? (a) 11/25 (b) 12/25 (c) 1/5 (d) 2/5 (e) 13/25

Question 3: A sample of size 3 is drawn at random and without replacement from the set {1, 2, 3, 4, 5}. What is the probability that the range of the sample is equal to 3? (a) 1/5 (b) 24/125 (c) 2/10 (d) 3/10 (e) 2/5

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Question 4: Consider a special die with P(1) = P(3) = P(5) = 1/9 and P(2) = P(4) = P(6) = 2/9. If we roll this die, what is the probability that the number is a prime number? (a) 3/9 (b) 4/9 (c) 5/9 (d) 1/2 (e) 1/3

Question 5: Suppose it is known that 23% of countries are classified as large, 19% of countries are classified as developed and 17% of countries are classified as both large and developed. What is the probability that a country selected at random is classified as large or developed? (a) 0.37 (b) 0.49 (c) 0.40 (d) 0.42 (e) 0.25

Question 6: Suppose the probability that an American has traveled to Canada is 0.38, to Mexico is 0.27, and to both countries is 0.05. What is the probability that an America selected at random has not traveled to either country? (a) 0.40 (b) 9.45 (c) 0.50 (d) 0.60 (e) 0.65

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Question 7: Common sources of caffeine are coffee, tea, and cola drinks. Suppose that 55% of a population drink coffee, 25% drink tea, and 45% drink cola. Also suppose 15% drink both coffee and tea, 5% drink all three, 25% drink both coffee and cola, and 5% drink only tea. What percent of the population drink ONLY one of coffee, tea or cola? (a) 30% (b) 35% (c) 40% (d) 45% (e) 50%

Question 8: Parts manufactured by an assembly plant are either produced by line A or by line B. The parts are also either defective or not defective. Suppose it is determined that 28% of all parts are defective, 70% of all parts are from Line A, and 8% of all parts are from line A and are defective. If you randomly select a part from line B, what is the probability it is defective? (a) 0.286 (b) 0.886 (c) 0.196 (d) 0.667 (e) 0.084

Question 9: An urn contains 10 red chips, 6 black chips, and 2 blue chips. You are to randomly select 2 chips without replacement. You win the game if both chips are black. What is the probability that you win? (a) 0.111 (b) 0.667 (c) 0.098 (d) 0.333 (e) 0.227

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Question 10: A quality inspector selects a sample of two items at random without replacement from a collection of 10 items, of which 4 have excellent quality, 3 have good quality, 2 have poor quality and one is defective. What is probability that the sample only contains items that are either excellent or good quality? (a) 0.15 (b) 0.23 (c) 0.30 (d) 0.47 (e) 0.55

Question 11: Consider two urns, labelled #1 and #2. Suppose urn #1 has 5 red and 7 blue balls and urn #2 has 6 red and 12 blue balls. If we pick three balls randomly from each of the two urns, what is the probability that all six chosen balls are the same color? (a) 0.022 (b) 0.044 (c) 0.088 (d) 0.110 (e) 0.130

Question 12: Suppose we roll two fair six-sided dice, one red and one blue. Let A be the event that the two dice show the same value and B be the event that the red die shows 4. Which of the following statements is TRUE ? (a) Events A and B are independent and mutually exclusive. (b) Events A and B are independent but they are not mutually exclusive. (c) Events A and B are not independent but they are mutually exclusive. (d) Events A and B are neither independent nor mutually exclusive. (e) Events A and B are only mutually exclusive.

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Question 13: If these three components are independent and each 95% reliable, what is the reliability of the system? (a) 0.732 (b) 0.762 (c) 0.857 (d) 0.925 (e) 0.995

Question 14: You play tennis regularly with a friend and, from past experience, you believe that the outcome of each match is independent. For any given match, you have a probability of 0.9 of winning. Find the probability that you lose at least one of the next four matches. (a) 0.0001 (b) 0.1000 (c) 0.3439 (d) 0.6561 (e) 0.9000

Question 15: You play tennis regularly with a friend who cannot play tennis very well. From past experience, you believe that the outcome of each match is independent. For any given match, you have a probability of 0.9 of winning. Suppose you and your friend decided to play tennis until your friend wins once or you win 3 times. What is the probability that you will play three matches? (a) 0.080 (b) 0.263 (c) 0.641 (d) 0.729 (e) 0.810

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Question 16: A laboratory test is 99% effective in detecting a certain disease when it is, in fact, present. However, the test yields a “false positive” result for 5% of the healthy persons tested. [That is, if a healthy person is tested, the probability that the test will indicate (incorrectly) that the person has a disease is 0.05.] If 1.5% of the population actually has the disease, what is the probability that a person randomly chosen person from the population has the disease if the test result is positive in his/her case? (a) 0.15 (b) 0.23 (c) 0.56 (d) 0.65 (e) 0.72

Question 17: A recent Maryland safety study found that in 77% of all accidents the derivers was wearing a seat belt. Accident reports indicate that 92% of those wearing seat belts escaped serious injury, but only 63% of the non-belted drivers were escaped serious injury. What is the probability that a driver is non-belted given that he injured in an accident? (a) 0.19 (b) 0.28 (c) 0.58 (d) 0.66 (e) 0.75

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