Question

$A$ and $B$ are seeking admission into $IIT$. If the probability for A to be selected is 0.5 and both to be selected is 0.3. Then atmost probability of $B$ is

• A. $0.9$
• B. $0.8$
• C. $0.6$
• D. $0.4$

Answer 1

The correct option is B $0.8$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow P\left(B\right)=P(A\cup B)-P\left(A\right)+P(A\cap B)$
$\Rightarrow P\left(B\right)=P(A\cup B)-0.5+0.3\le 1-0.2=0.8$
$P\left(B\right)\le 0.8$