The National Public Radio show Car Talk used to have a feature called "The Puzzler." Listeners were asked to send in answers to some puzzling questions-usually about cars but sometimes about probability (which, of course, must account for the incredible popularity of the program!). Suppose that for a car question, 110 answers were submitted, of whi

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The National Public Radio show Car Talk used to have a feature called "The Puzzler." Listeners were asked to send in answers to some puzzling questions-usually about cars but sometimes about probability (which, of course, must account for the incredible popularity of the program!). Suppose that for a car question, 110 answers were submitted, of which 30 are correct. (a) Suppose that the hosts randomly select two answers from those submitted with replacement. (For purposes of this problem, keep at least four digits to the right of the decimals.) Calculate the probability that both selected answers are correct. (b) Suppose now that the hosts select the answers at random but without replacement. Use conditional probability to evaluate the probability that both answers selected are correct.

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How does this probability compare to the one computed in Part (a)?

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2 * with replacement

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