Question

If $A$ and $B$ are two events such that $P ( A )=\frac{1}{3}, P ( B )=\frac{1}{5}$ and $P ( A \cup B )=\frac{1}{2}$, then $P \left( A \mid B ^{\prime}\right)+ P \left( B \mid A ^{\prime}\right)$ 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∪B)=P(A)+P(B)−P(A∩B)
21​=31​+51​−P(A∩B)
P(A∩B)=301​
P(BA​)+P(AB​)=P(B)P(A∩B)​+P(A)P(B∩A)​
=1−P(B)P(A)−P(A∩B′)​+1−P(A)P(B)−P(A∩B)​
=54​31​−301​​+32​51​−301​​=85​