Question

Given that the events $A$ and $B$ are such that $P\left(A\right)=\frac{1}{2}$ , $P(A\cup B)=\frac{3}{5}$ and $P\left(B\right)=p$. The value of p if they are independent events is:

• A. $\frac{1}{5}$
• B. $\frac{2}{5}$
• C. $\frac{1}{4}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A $\frac{1}{5}$

$P(A\cup B)=\frac{3}{5}=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)\Rightarrow \frac{3}{5}=\frac{1}{2}+p-\frac{p}{2}p=\frac{1}{5}$