Florida International University

Business Statistics - STA 2023

Ms. Laura Reisert Instructor

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Chapter 3-C Supplementary Exercises

1. In college basketball games a player may be afforded the opportunity to shoot two consecutive foul shots (free throws).
   a. Suppose a player who scores on 70% of his foul shots has been awarded two free throws. If the two throws are considered independent, what is the probability that the player scores on both shots? Exactly one? Neither shot?
   b. Suppose a player who scores 70% on his first attempted foul shots has been awarded two free throws, and the outcome of the second shot is dependant on the result of the first shot. In fact, if this player makes the first shot, he makes 80% of the second shots, and if he misses the first shot, he makes 60% if the second shots. In this case, what is the probability that the player scores on both shots? Exactly one? Neither shot?
   c. In parts a and b, we considered two ways of modeling probability a basketball player scores on two consecutive foul shots. Which model do you think is a more realistic attempt to explain the outcome of shooting foul shots, i.e., do you think two consecutive foul shots are independent or dependent? Explain.
2. A manufacturer of 35-mm cameras knows that a shipment of thirty cameras sent to a large discount store contains 6 defective cameras. The manufacturer also knows the store will choose two of the cameras at random, test them, and accept the shipment if neither is defective.
   a. What is the probability that the first camera chosen by the store will be defective?
   b. Given that the first camera chosen passed inspection, what is the probability that the second camera chosen will fail inspection?
   c. What is the probability the shipment is accepted?
3. The probability that a mini-computer salesperson sells a computer to a prospective customer on the first visit to the customer is .3. If the salesperson fails to make the sale on the first visit, the probability that the sale will be made on the second visit is .55. The salesperson never visits a prospective customer more than twice. What is the probability that the salesperson will make a sale to a particular customer?
4. Seventy percent of all women who submit to pregnancy tests are really pregnant. A certain pregnancy test gives a false positive result with probability .01 and a valid positive result with probability .98. If a particular woman's test is positive, what is the probability that she really is pregnant?
5. A small catsup company has two bottling machines. Machine A produces 60% of the bottles and machine B produces 40%. One out of every twenty bottles filled by A is rejected for some reason, while one out of every twenty-five bottles from B is rejected. What proportion of bottles is rejected? What is the probability that a bottle comes from machine A, if we know that it is accepted?