A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{4}\]
D) \[\frac{1}{6}\]
Correct Answer: A
Solution :
Given that, \[P(A)=P(B)=x\] and \[P(A\cap B)=P(A'\cap B')=1/3\] \[\therefore \] \[P(A'\cap B')=1-P(A\cup B)=1/3\] \[\Rightarrow \] \[P(A\cup B)=2/3\] Now, \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \] \[\frac{2}{3}=x+x-\frac{1}{3}\] \[\Rightarrow \] \[2x=1\] \[\Rightarrow \] \[x=\frac{1}{2}\]
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