The national public radio show car talk has a feature called "the puzzler." listeners are 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 suppose that for a car question, 600 answers are submitted, of which 50 are correct. suppose also that the hosts randomly select two answers from those submitted with replacement. (for purposes of this problem, keep at least five digits to the right of the decimals.)

(a) 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.