91Ó°ÊÓ

A doctor knows from experience that \(10 \%\) of the patients to whom she gives a certain drug will have undesirable side effects. Find the probabilities that among the 10 patients to whom she gives the drug: a. At most two will have undesirable side effects. b. At least two will have undesirable side effects.

A box contains 10 items, of which 3 are defective and 7 are nondefective. Two items are randomly selected, one at a time, with replacement, and \(x\) is the number of defectives in the sample of two. Explain why \(x\) is a binomial random variable.

Bill has completed a 10-question multiple-choice test on which he answered 7 questions correctly. Each question had one correct answer to be chosen from five alternatives. Bill says that he answered the test by randomly guessing the answers without reading the questions or answers. a. Define the random variable \(x\) to be the number of correct answers on this test, and construct the probability distribution if the answers were obtained by random guessing. b. What is the probability that Bill guessed 7 of the 10 answers correctly? c. What is the probability that anybody can guess six or more answers correctly? d. Do you believe that Bill actually randomly guessed as he claims? Explain.