A student appears for test I, II III. The student is successful if he passes either in test I and II or test I and III. The probabilities of the student passing in tests I, II, III are p, q, q/2 respectively. If the probability that the student is successful is 1/2, then find the relation between p and q.

Given , The probabilities of the student passing in tests I, II, III are p, q, q/2 respectively and for success he must pass either in test I and II or in test I and III so

P(s)= Probability of success = pass either in test I and II or in test I and III

= p*q + p*(q/2) = 1/2 (given)

3pq/2 = 1/2

pq = 1/3

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