Question

If $A$ and $B$ are mutually exclusive events and if $p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21},$ then $P(A)$ is equal to

• A. $\frac{1}{7}$
• B. $\frac{4}{7}$
• C. $\frac{2}{7}$
• D. $\frac{5}{7}$

Answer 1

Answer: (C)

$\frac{2}{7}$

Answer 2

We have $p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21}$
For mutually exclusive events A and B, we get $p(A\cup B)=p(A)+p(B)$
$\Rightarrow$ $p(A)=p(A\cup B)-p(B)$
$=\frac{13}{21}-\frac{1}{3}$
$=\frac{13-7}{21}=\frac{6}{21}=\frac{2}{7}$
$\therefore$ $p(A)=\frac{2}{7}$