Question

If A and B are two events such that $P(A)=\frac1{3},P(B)=\frac1{5}$ and $P(A∪B)=\frac1{2}$ then $P(\frac{A}{B'}) + P(\frac{B}{A'})$ is equal to

• A. $\frac{3}4$
• B. $\frac{5}8$
• C. $\frac{5}4$
• D. $\frac{7}8$

Answer 1

Answer: (B)

$\frac{5}8$

Answer 2

$P(A)=\frac1{3},P(B)=\frac1{5}$ and $P(A∪B)=\frac1{2}$

$P(A∩B)=\frac1{3}+\frac1{5}-\frac1{2}=\frac1{30 }$

Now,
$P(\frac{A}{B'})+P(\frac{B}{A'}) =$ $\frac{P(A∩B')}{P(B')}+\frac{P(B∩A')}{P(A')}$

$=\frac{\frac9{30}}{\frac{4}{5}} \- \frac{\frac5{30}}{\frac2{3}}$

$=\frac5{8}$