A) \[\frac{3}{5}\]
B) \[\frac{1}{6}\]
C) \[\frac{2}{3}\]
D) \[\frac{3}{8}\]
Correct Answer: D
Solution :
[d] Let A = the even that a five occur Let B = the even that a man report that it is five \[\therefore P(A/B)=\frac{P(A\cap B)}{P(B)}\] Now, \[P\left( A\cap B \right)=P\left( A \right).P\left( B \right)\] (\[\therefore \]Both event be independent) \[=\frac{1}{8}+P({A}')\times P({B}')\] \[=\frac{1}{8}+\frac{1}{4}\times \frac{5}{6}=\frac{1}{8}+\frac{5}{24}=\frac{3+5}{24}\] \[=\frac{1}{6}=\frac{8}{24}=\frac{1}{3}\] \[\therefore P\left( \frac{A}{B} \right)=\frac{P(A\cap B)}{P(B)}=\frac{1/8}{1/3}=\frac{3}{8}\] Hence, option [d] is correct.
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