Probability Question 129
Question: The probability that at least one of the events A and B occurs is 3/5. If A and B occur simultaneously with probability 1/5, then $ P({A}’)+P({B}’) $ is
[DCE 2002]
Options:
A) $ \frac{2}{5} $
B) $ \frac{4}{5} $
C) $ \frac{6}{5} $
D) $ \frac{7}{5} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ P(A\cup B)=\frac{3}{5} $ and $ P(A\cap B)=\frac{1}{5} $
We know $ P(A\cup B)=P(A)+P(B)-P(A\cap B) $
$ \frac{3}{5}=1-P(\overline{A})+1-P(\overline{B})-\frac{1}{5} $
$ 2-\frac{4}{5}=P(\overline{A})+P(\overline{B}) $
$ \Rightarrow $
$ P(\overline{A})+P(\overline{B})=\frac{6}{5} $ .
BETA
