Question

Given that $A$ and $B$ are two events such that $P(B)=\frac{3}{5}P(A/B)=\frac{1}{2}$ and $P(A\cup B)=\frac{4}{5}$ then $P(A)=$

• A. $\frac{3}{10}$
• B. $\frac{1}{2}$
• C. $\frac{1}{5}$
• D. $\frac{3}{5}$

Answer 1

Answer: (B)

$\frac{1}{2}=P\frac{(A\cap B)}{\frac{3}{5}}$
$\Rightarrow P(A\cap B)=\frac{3}{10}$
$\frac{4}{5}=\frac{3}{5}+P(A)-\frac{3}{10}$
$\Rightarrow P(A)=\frac{1}{2}$