Question

If A and B are any two events such that $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{1}{3},andP(A\cap B)=\frac{1}{4},thenP\left(A^{\prime }/B^{\prime }\right)=$

• A. 5/6
• B. 5/12
• C. 5/8
• D. 1/2

Answer 1

The correct option is C

5/8

$P(A\cup B)=\frac{1}{2}+\frac{1}{3}-\frac{1}{4}=\frac{6+4-3}{12}=\frac{7}{12}\therefore P\left(A^{\prime }/B^{\prime }\right)=\frac{P(A^{\prime }\cap B^{\prime })}{P\left(B^{\prime }\right)}=\frac{1-P(A\cup B])}{1-P\left(B\right)}=\frac{7/13}{1-\frac{1}{3}}=\frac{\frac{5}{12}}{2/3}=\frac{5}{8}$