Quantitative Methods for Business Cha 2—Introduction to Probability PROBLEM

1745 WordsFeb 23, 20147 Pages
Chapter 2—Introduction to Probability PROBLEM 1. A market study taken at a local sporting goods store showed that of 20 people questioned, 6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and camping stoves. Let: Event A = owns a tent Event B = owns a sleeping bag Event C = owns a camping stove and let the sample space be the 20 people questioned. a. Find P(A), P(B), P(C), P(A C), P(B C). b. Are the events A and C mutually exclusive? Explain briefly. c. Are the events B and C independent events? Explain briefly. d. If a person questioned owns a tent, what is the probability he also owns a camping stove? e. If two people…show more content…
Develop a joint probability table and show the marginal probabilities. b. What is the probability of a household whose income exceeds $60,000 and who rejects the offer? c. If income is  $60,000, what is the probability the offer will be accepted? d. If the offer is accepted, what is the probability that income exceeds $60,000? ANSWER: a. Income  $60,000 Income > $60,000 Total Accept offer .100 .075 .175 Reject offer .525 .300 .825 Total .625 .375 1.000 b. .3 c. .16 d. .4286 8. A medical research project examined the relationship between a subject's weight and recovery time from a surgical procedure, as shown in the table below. Underweight Normal weight Overweight Less than 3 days 6 15 3 3 to 7 days 30 95 20 Over 7 days 14 40 27 a. Use relative frequency to develop a joint probability table to show the marginal probabilities. b. What is the probability a patient will recover in fewer than 3 days? c. Given that recovery takes over 7 days, what is the probability the patient is overweight? ANSWER: a. Underweight Normal weight Overweight Total Less than 3 days .024 .06 .012 .096 3 to 7 days .120 .38 .080 .580 Over 7 days .056 .16 .108 .324 Total .200 .60 .200 1.00 b. .096 c. 27/81 = .33 9. It is estimated that 3% of the athletes competing in a large tournament are users of an

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