Statistics And Probability Question 549

Question: If $ P(A)=\frac{1}{2},P(B)=\frac{1}{3} $ and $ P(A\cap B)=\frac{7}{12}, $ then the value of $ P({A}’\cap {B}’) $ is

Options:

A) $ \frac{7}{12} $

B) $ \frac{3}{4} $

C) $ \frac{1}{4} $

D) $ \frac{1}{6} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ P({A}’\cap {B}’)=1-P(A\cup B) $ $ =1-( \frac{1}{2}+\frac{1}{3}-\frac{7}{12} )=1-\frac{1}{4}=\frac{3}{4} $ .