Browse Questions

For two independent events A and B $P( A \cap B ) = \large\frac{3}{25}\: P(A' \cap B) = \large\frac{8}{25}$ then $P(B) =$

$\begin {array} {1 1} (1)\;\large\frac{3}{11} & \quad (2)\;\large\frac{7}{25} \\ (3)\;\large\frac{11}{25} & \quad (4)\;None\: of \: these \end {array}$

Since A and B are independent
$P ( A \cap B ) = P(A)P(B)$
$P(A' \cap B ) = P(A') P(B)$
$\Rightarrow P(A)P(B)= \large\frac{3}{25}$
$(1-P(A))P(B) = \large\frac{8}{25}$
$P (B) = \large\frac{11}{25}$
Ans : (3)