Question

If A and B are two events such that $P\left(A\right)=\frac{3}{8},P\left(B\right)=\frac{5}{8}$ and $P(A\cup B)=\frac{3}{4}$, then $P(A\cap \overline{B})=$

• A. $\frac{5}{8}$
• B. $\frac{3}{8}$
• C. $\frac{1}{8}$
• D. $\frac{2}{8}$

Answer 1

Answer: (C)

$\frac{1}{8}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\frac{3}{4}=\frac{3}{8}+\frac{5}{8}-P(A\cap B)$
$P(A\cap B)=\frac{1}{4}$
$P(A\cap \overline{B})=P\left(A\right)-P(A\cap B)$
$P(A\cap \overline{B})=\frac{3}{8}-\frac{1}{4}=\frac{1}{8}$