Question

If $A$ and $B$ are mutually exclusive events with $ P(A)=\frac{1}{2}\times P(B) $ and $ A\cup B=S, $ (total sample space) then $ P(A) $ is equal to

• A. $ \frac{2}{3} $
• B. $ \frac{1}{3} $
• C. $ \frac{1}{4} $
• D. $ \frac{3}{4} $

Answer 1

Answer: (B)

Given, $ P(A)=\frac{1}{2}P(B) $
$ \Rightarrow $ $ P(B)=2P(A) $
and $ A\cup B=S $
$ \therefore $ $ P(A\cup B)=P(S)=1 $
$ \Rightarrow $ $ P(A)+P(B)=1 $
$ [\because \,\,P(A\cap B)=0] $
$ \Rightarrow $ $ P(A)+2P(A)=1 $
$ \Rightarrow $ $ P(A)=\frac{1}{3} $