Statistics And Probability Question 42
Question: The probability that a particular day in the month of July is a rainy day is ¾. Two person whose credibility are 4/5 and 2/3. Respectively, claim that 15 July was rainy day. The probability that it was really a rainy day is
Options:
A) $ \frac{12}{13} $
B) $ \frac{11}{12} $
C) $ \frac{24}{25} $
D) $ \frac{29}{30} $
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Answer:
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}. $
BETA
