Question

A student appears for test I, II and III. The student is successful if he passes either in test I, II or I, III. The probability of the student passing in test I, II and III are respectively p, q and $1/2$. If the probability of the student to be successful is $1/2$ then

Answer 1

Let P(S) = probability of success = $\frac{1}{2}$

Given:

The probability of student passing in the tests I, II, III are $p,q,\frac{1}{2}$ respectively and for success, he must pass either in test I and II or in test I and III. So,

P(S) = pass either in test I and II or in test I and III = $\frac{1}{2}$

$⟹=p\times q+p\times \frac{1}{2}=\frac{1}{2}⟹\frac{2pq+p}{2}=\frac{1}{2}⟹2pq+p=1$