| Easy | Probability |
A father claims about snowfall last night. First daughter tells that the probability of snowfall on a particular night is 1/8. Second daughter tells that 5 out of 6 times the father is lying! What is the probability that there actually was a snowfall?
Hint
Conditional Probability or Baye's Theorem
Solution
Let S = Snowfall occurred, and C = Claim
Probability of (Snowfall given Claim) = P(S | C) = P(C|S)*P(S)/P(C)
Now, P(C|S) = 1/6, P(S) = 1/8
P(C ) = P(true claim) + P(False Claim) = P(C|S)*P(S) + P( false claim|no snow)*P(no snow)
This is same as [1/6*1/8]/[ 1/6*1/8 + 7/8*5/6] = 1/36
Probability of (Snowfall given Claim) = P(S | C) = P(C|S)*P(S)/P(C)
Now, P(C|S) = 1/6, P(S) = 1/8
P(C ) = P(true claim) + P(False Claim) = P(C|S)*P(S) + P( false claim|no snow)*P(no snow)
This is same as [1/6*1/8]/[ 1/6*1/8 + 7/8*5/6] = 1/36
Source: Written Test
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