Question

For two independent events $A$ and $B$ if $P\left(A\right)=\frac{3}{5}$ and $P(A\cap B)=\frac{4}{9}$ then find $P\left(B\right)$.

Answer 1

Given, For two independent events $A$ and $B$ if $P\left(A\right)=\frac{3}{5}$ and $P(A\cap B)=\frac{4}{9}$.

Since $A$ and $B$ are independent then $P(A\cap B)=P\left(A\right).P\left(B\right)$.

or, $\frac{4}{9}=\frac{3}{5}.P\left(B\right)$

or, $P\left(B\right)=\frac{20}{27}$.