Question

Given two independent events A and B such that $P\left(A\right)=0.3,$ $P(A\cap B)=0.1$. Find $P\left(A\cap B^{\prime }\right)$

• A. $0.1$
• B. $0.2$
• C. $0.15$
• D. $0.3$

Answer 1

The correct option is B $0.2$

Given $P\left(A\right)=0.3,P(A\cap B)=0.1$

If $A$ and $B$ are independent events, $P(A\cap B)=P\left(A\right)P\left(B\right)$

$\Rightarrow P\left(B\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{0.1}{0.3}=\frac{1}{3}$

If $A$ and $B$ are independent events,

$P(A\cap B^{\prime })=P\left(A\right)\times P\left(B^{\prime }\right)$

$=P\left(A\right)(1-P\left(B\right))$

$=0.3(1-\frac{1}{3})$

$=0.3\times \frac{3-1}{3}=0.3\times \frac{2}{3}=0.1\times 2=0.2$