A) \[\frac{5}{12}\]
B) \[\frac{3}{8}\]
C) \[\frac{5}{8}\]
D) \[\frac{1}{4}\]
Correct Answer: A
Solution :
\[P\,(A\cup B)\,=\frac{3}{4},\] \[P(A\cap B)=\frac{1}{4}\] \[P(\bar{A})\,=\frac{2}{3}\,\,\Rightarrow \] \[P(A)=\,\frac{1}{3}\] \[\therefore \]\[P(A\cap B)\,=\,P(A)\,+P\,(B)\,-P(A\cup B)\] \[\frac{1}{4}=\frac{1}{3}+P(B)\,-\frac{3}{4}\] Þ \[P(B)\,=\frac{2}{3}\] \[P(\bar{A}\cap \,B)\]= \[P(B)-\,P\,(A\cap B)\]\[=\frac{2}{3}-\frac{1}{4}=\frac{8-3}{12}=\frac{5}{12}.\]You need to login to perform this action.
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