Question

If the events A and B are independent if $P\left(A^{\prime }\right)=\frac{2}{3}$ and $P\left(B^{\prime }\right)=\frac{2}{7}$, then $P(A\cap B)$ is equal to.

• A. $\frac{5}{21}$
• B. $\frac{3}{21}$
• C. $\frac{4}{21}$
• D. $\frac{1}{21}$

Answer 1

Answer: (A)

$\frac{5}{21}$

$P\left(A\right)=1-P\left(A^{\prime }\right)=1-\frac{2}{3}=\frac{1}{3}$

and $P\left(B\right)=1-P\left(B^{\prime }\right)=1-\frac{2}{7}=\frac{5}{7}$

Now if A and B are independent event then,

$P(A\cap B)=P\left(A\right)P\left(B\right)=\frac{1}{3}\cdot \frac{5}{7}=\frac{5}{21}$