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} $
• E. $ \frac{6}{7} $

Answer 1

Answer: (C)

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} $