Probability Question 357
Question: For two mutually exclusive events A and B, $ P(A)=0.2 $ and $ P(\bar{A}\bigcap B)=0.3. $ What is $ P(A|(A\bigcup B)) $ equal to-
Options:
A) $ \frac{1}{2} $
B) $ \frac{2}{5} $
C) $ \frac{2}{7} $
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
Event A and B are mutually exclusive.
Hence $ P(A\cap B)=\phi =0 $
$ \therefore P(A\cup B)=P(A)+P(B) $ - (1) $ P(A)=0.2 $ [Given] $ P(B)=P(\bar{A}\cap B)+P(A\cap B) $
$ P(B)=P(\bar{A}\cap B) $
$ [\because P(A\cap B)=0] $
$ =0.3 $
$ P(A\cup B)=0.2+0.3=0.5 $
$ P(A|A\cup B)=\frac{P(A)}{P(A\cup B)}=\frac{0.2}{0.5}=\frac{2}{5} $
$ P(A|(A\cup B))=\frac{2}{5} $
BETA
