question_answer

Let A and B are events of an experiment and \[P(A)=1/4,\,\,P(A\cup B)=1/2\] then value of \[P(B/{{A}^{c}})\] is

A) 2/3       

B) 1/3

C) 5/6                   

D) 1/2

Correct Answer: B

Solution :

[b] \[P(A)=\frac{1}{4},P(A\cup B)=\frac{1}{2}\] \[\frac{P(A\cup B)-P(A)}{1-P(A)}=\frac{P(A\cup B)-P(A)}{1-P(A)}\] \[[\therefore P(A\cup B)+P(B)-P(A\cap B)]\] \[=\frac{\frac{1}{2}-\frac{1}{4}}{1-\frac{1}{4}}=\frac{1}{4}\times \frac{4}{3}=\frac{1}{3}\]