Question

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

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

Answer 1

The correct option is C $\frac{7}{10}$

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