A) \[\frac{12}{13}\]
B) \[\frac{11}{12}\]
C) \[\frac{24}{25}\]
D) \[\frac{29}{30}\]
Correct Answer: C
Solution :
[c] Let events A : Event that first man speak truth B: Event that second man speaks truth R: Day is rainy \[\therefore P(A)=\frac{4}{5},P(B)=\frac{2}{3},P(R)=\frac{3}{4}\] \[\therefore \] Required probability \[=\frac{P(A\cap B).P(R)}{P(A\cap B).P(R)+P(A'\cap B,).P(R')}\] \[=\frac{\frac{4}{5}\times \frac{2}{3}\times \frac{3}{4}}{\frac{4}{5}\times \frac{2}{3}\times \frac{1}{5}+\frac{1}{3}\times \frac{1}{4}}=\frac{24}{25}.\]
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