Question

A student appears in test I, II and III. The student is successful if he passes either in test I and II or in test I and III. The probabilities that the student is successful in Tests I, II, III are p,q,$\frac{1}{2}$.If the probability that the student is successful is 1/2, then find the relation between p and q.

• A. $p=q=1$
• B. $p=q=\frac{1}{2}$
• C. $p=1,q=0$
• D. $p=1,q=\frac{1}{2}$

Answer 1

The correct option is C $p=1,q=0$

The student will be successful in three cases.
Now,$P$($I,II,$ not $III$)$+P$($I,III,$ not $II$)$+P$($I,II,III,$)
$=p.q.(1-\frac{1}{2})+p\frac{1}{2}(1-q)+p.q\frac{1}{2}$
$=\frac{1}{2}pq+\frac{1}{2}p-\frac{1}{2}pq+\frac{1}{2}pq$
$=\frac{1}{2}p(1+q)=\frac{1}{2}$ (given) $\Rightarrow p(1+q)=1$
This condition will be satisfied when $p=1,q=0.$