Statistics And Probability Question 575
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}=P(A)+P(B)-\frac{1}{5} $ $ P(A)+P(B)=\frac{3}{5}+\frac{1}{5} $ $ \Rightarrow $ $ P(\overline{A})+P(\overline{B})=\frac{3}{5} $
BETA
