If the probability of rain on any given day in Chicago during the summer is 20%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7 inclusive? Choose the correct choice from the following options:
A) 2/25
B) 3/125
C) 7/125
D) 12/625
E) 16/625
One possible case is: rainy-rainy-rainy-not rainy.   The probability of this case is 1/5*1/5*1/5*4/5 = 4/625   The number of possible cases is 4C3 = 4.   P(exactly 3 rainy days) = 4*4/625 = 16/625   The answer is 16/625.
<result>E</result>
If the probability of rain on any given day in Chicago during the summer is 20%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7 inclusive?