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.

Let P(s)= Probability of success 
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