If the probability of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
8/125
2/25
5/16
8/25
3/4
8/125
2/25
5/16
8/25
3/4
answer is 5/16
Choosing 3 days out of 5 is 5C3 = 5!/(3! x 2!) = 10
3 days of rain = P(A) = 1/2 x 1/2 x 1/2 = 1/8
and 2 days of no rain is P(B) = (1-1/2)X(1-1/2) = 1/4
P(A and B) = P(A) X P(B) = 1/32
So total number of such cases is 10 hence probability is
10 x 1/32 = 5/16
