# Question

To get answers to sensitive questions, we some-times 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 smoke marijuana. We construct 20 flash cards, write “ I smoke marijuana at least once a week” on 12 of the cards, where 12 is an arbitrary choice, And “ I do not smoke marijuana at least once a week” on the others. Then, we let each student (in the sample interviewed) select one of the 20 cards at random And respond “ 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(M) , the probability that a student randomly selected at that university smokes marijuana at least once a week.

(b) If 106 of 250 students Answered “ yes” under these conditions, use the result of part (a) And 106/250 as an estimate of P(Y) to estimate P(M) .

(a) Establish a relationship between P(Y) , the probability that a student will give a “ yes” response, And P(M) , the probability that a student randomly selected at that university smokes marijuana at least once a week.

(b) If 106 of 250 students Answered “ yes” under these conditions, use the result of part (a) And 106/250 as an estimate of P(Y) to estimate P(M) .

## Answer to relevant Questions

Use the Venn diagram of Figure 2.7 And the method by which we proved Theorem 2.7 to prove Theorem 2.8. Figure 2.7 Subjective probabilities may be determined by exposing persons to risk- taking situations And finding the odds at which they would consider it fair to bet on the outcome. The odds are then converted into probabilities by ...Show that if events A And B are dependent, then events A And B' are dependent. Show that P(A ∪ B) ≥ 1- P(A') - P(B') for Any two events A And B defined in the sample space S. If S = {x| 0< x< 10}, M = {x| 3< x ≤ 8}, And ∩ = {x| 5< x< 10}, find (a) M. N; (b) M ∩ N; (c) M ∩ N' ; (d) M ∪ N.Post your question

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