Question

A student appears for tests I, II and III. The student is successful if he passes either in test I and II or in I and III. The probability of student passing in tests I,II, III are respectively $p,\frac{1}{2},\frac{1}{2}$. If the probability that student is successful is $\frac{2}{3}$, then p is

• A. $\frac{8}{9}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{2}{9}$

Answer 1

The correct option is A $\frac{8}{9}$

$\frac{2}{3}=$ Passes in I,II not III + Passes in I, III not II + Passes in I, II, III
$\Rightarrow \frac{2}{3}=p.\frac{1}{2}.\frac{1}{2}+p.\frac{1}{2}.\frac{1}{2}+p.\frac{1}{2}.\frac{1}{2}$
$\Rightarrow \frac{2}{3}=\frac{3p}{4}\Rightarrow p=\frac{8}{9}$