Probability Question 262
Question: A and B are two independent events. The probability that both A and B occur is $ \frac{1}{6} $ and the probability that neither of them occurs is $ \frac{1}{3} $ . Then the probability of the two events are respectively
[Roorkee 1989]
Options:
A) $ \frac{1}{2} $ and $ \frac{1}{3} $
B) $ \frac{1}{5} $ and $ \frac{1}{6} $
C) $ \frac{1}{2} $ and $ \frac{1}{6} $
D) $ \frac{2}{3} $ and $ \frac{1}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ P(A\cap B)=P(A).P(B)=\frac{1}{6} $
$ P(\bar{A}\cap \bar{B})=\frac{1}{3}=1-P(A\cup B) $
$ \Rightarrow \frac{1}{3}=1-[P(A)+P(B)]+\frac{1}{6}\Rightarrow P(A)+P(B)=\frac{5}{6}. $
Hence $ P(A) $ and $ P(B) $ are $ \frac{1}{2} $ and $ \frac{1}{3}. $
BETA
