Probability Question 231
Question: If two events A and B are such that $ P(A+B)=\frac{5}{6}, $
$ P(AB)=\frac{1}{3} $ and $ P(\bar{A})=\frac{1}{2}, $ then the events A and B are
Options:
A) Independent
B) Mutually exclusive
C) Mutually exclusive and independent
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
We have $ P(A+B)=P(A)+P(B)-P(AB) $
$ \Rightarrow \frac{5}{6}=\frac{1}{2}+P(B)-\frac{1}{3}\Rightarrow P(B)=\frac{4}{6}=\frac{2}{3} $
Thus, $ P(A).P(B)=\frac{1}{2}\times \frac{2}{3}=\frac{1}{3}=P(AB) $
Hence events $ A $ and $ B $ are independent.
BETA
