To get answers to sensitive questions, we sometimes use a method called the randomized response technique. Suppose, for instance, that we want to determine what percentage of the students at a large university take ketamine. We construct 20 flash cards, write 'I take ketamine at least once a week' on 12 of the cards (where 12 is an arbitrary choice) and 'I do not take ketamine at least once a week' on the others. Then we let each student (in the sample interviews) select one of the 20 cards at random, and response yes or no without divulging the question.

(a) Establish a relationship between P(Y ), the probability that a student will give a yes response, and P(K), the probability that a student randomly selected at the university takes ketamine at least once a week.

(b) If 110 of 250 students answered yes under these conditions, use the result of part (a) and 110/250 as an estimate of P(Y ) to estimate P(K).