Question

For any two events $A$ and $B$, if $P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P\left(B\right)=\frac{1}{2}$, then $P\left(A\right)$ is:

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{1}{3}$
• D. none of these

Answer 1

The correct option is B $\frac{2}{3}$

Given, $P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P\left(B\right)=\frac{1}{2},$

$\because P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\therefore P\left(A\right)=\frac{5}{6}-\frac{1}{2}+\frac{1}{3}$

$=\frac{5-3+2}{6}=\frac{4}{6}=\frac{2}{3}$