JEE Advance - Mathematics (1986 - No. 28)
A student appears for tests, $$I$$, $$II$$ and $$III$$. The student is successful if he passes either in tests $$I$$ and $$II$$ or tests $$I$$ and $$III$$. The probabilities of student passing in tests $$I$$, $$II$$ and $$III$$ are $$p, q$$ and $${1 \over 2}$$ respectively. If the probability that the student is successful is $${1 \over 2}$$, then
$$p=q=1$$
$$p = q = {1 \over 2}$$
$$p=1,$$ $$q=0$$
$$p = 1,q = {1 \over 2}$$