Question

Suppose $A$ and $B$ are two events such that $P(A \cap B)=\frac{3}{25}$ and $P(B-A)=\frac{8}{25} .$ Then, $P(B)$ is equal to

• A. $\frac{11}{25}$
• B. $\frac{3}{11}$
• C. $\frac{1}{11}$
• D. $\frac{9}{11}$

Answer 1

Answer: (A)

Given, $P(A \cap B)=\frac{3}{25}$
$P(B-A) =\frac{8}{25}$
Then according to figure
$P(B)=P(A \cap B)+P(B-A)$
$P(B)=\frac{3}{25}+ \frac{8}{25}$
$\Rightarrow P(B)=\frac{11}{25}$