Question

If $A$ and $B$ are events of a random experiment such that $P(A\cup B)=\frac{4}{5},P(A\cup \bar{B})=\frac{7}{10}$ and $P(B)=\frac{2}{5},$ then $P(A)$ equals

• A. $\frac{9}{10}$
• B. $\frac{8}{10}$
• C. $\frac{7}{10}$
• D. $\frac{3}{5}$

Answer 1

Answer: (C)

Given, $P(\bar{A}\cup \bar{B})=P(\overline{A\cap B})=\frac{7}{10}$ ,
Since, $P(A\cap B)+P(\overline{A\cap B})=\frac{1}{3}$
$\Rightarrow PA\cap B=1-\frac{7}{10}=\frac{3}{10}$
Also, $P(A\cap B)=P(A)+P(B)-P(A\cap B)$
$\Rightarrow \frac{4}{5}=PA+\frac{2}{5}-\frac{3}{10}$
$\Rightarrow PA=\frac{4}{5}-\frac{2}{5}+\frac{3}{10}$
$=\frac{2}{5}+\frac{3}{10}=\frac{7}{10}$