The probability that a particular day in the month of July is a rainy day is `3/4` . Two person whose credibility and `4/5` and `2/3` , respectively, claim that 15th July was a rainy day. Find the probability that it was really a rainy day.

Answer

`24//25`

Explanation

Let events
A: Event that fiest man speaks truth
B: Event that second man speaks truth
R: Day is rainy
`thereforeP(A)=4/5,P(B)=2/3,P(R)=3/4`
`therefore` Required probability
`=(P(AnnB).P(R))/(P(AnnB).P(R)+P(A'nnB').P(R'))`
`=(4/5xx2/3xx3/4)/(4/5xx2/3xx3/4+1/5xx1/3xx1/4)=24/25`