A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{4}\]
D) None of these
Correct Answer: C
Solution :
\[P[B/(A\cup {{B}^{c}})]=\frac{P(B\cap (A\cup {{B}^{c}}))}{P(A\cup {{B}^{c}})}\] \[=\frac{P(A\cap B)}{P(A)+P({{B}^{c}})-P(A\cap {{B}^{c}})}\] \[=\frac{P(A)-P(A\cap {{B}^{c}})}{P(A)+P({{B}^{c}})-P(A\cap {{B}^{c}})}\]\[=\frac{0.7-0.5}{0.8}=\frac{1}{4}\].
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