A) \[\frac{8}{13}\]
B) \[\frac{7}{13}\]
C) \[\frac{6}{13}\]
D) \[\frac{4}{13}\]
Correct Answer: D
Solution :
[d] \[\because A,B\And C\]be exhaustive & mutually exclusive events. \[\therefore P\left( A\cup B\cup C \right)=P\left( A \right)+P\left( B \right)+P\left( C \right)\] \[1=x+\frac{3}{2}x+\frac{1}{2}\times \frac{3}{2}x\] (Say \[P\left( A \right)=x)\] \[1=x+\frac{3x}{2}+\frac{3x}{4}=\frac{4x+6x+3x}{4}\] \[\Rightarrow \frac{13x}{4}=1\Rightarrow x=\frac{4}{13}\]. i.e. \[P\left( A \right)x=\frac{4}{13}\]So, option [d] is correct.You need to login to perform this action.
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