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

• Correct answer
  A

  $\frac{11}{25}$
• B

  $\frac{3}{11}$
• C

  $\frac{1}{11}$
• D

  $\frac{9}{11}$

Solution

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

Hence, the correct answer is option: 'A'.