Question

Two events A and B are independent, if P(A)=3/5 and P(A∩B)=4/9 , then the value of P(B) is

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \:  - \begin{cases} &\sf{P(A) =\dfrac{3}{5} } \\ &\sf{P(A \: \cap \: B) = \dfrac{4}{9} } \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: find \:  - \begin{cases} &\sf{P(B)}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given that

$\rm :\implies\:P(A) = \dfrac{3}{5}$

and

$\rm :\implies\:P(A \: \cap \: B) = \dfrac{4}{9}$

Since,

• A and B are independent events.

$\boxed{ \rm :\implies\:\red{ \tt \: P(A \: \cap \: B) = P(A) \times P(B)}}$

$\rm :\implies\:\dfrac{4}{9} = \dfrac{3}{5} \times P(B)$

$\rm :\implies\:P(B) = \dfrac{20}{27}$