If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 9 inclusive? Choices:
A) 3/16
B) 5/16
C) 7/32
D) 11/32
E) 17/64
One possible case is: rainy-rainy-rainy-not rainy-not rainy-not rainy.   The probability of this case is (1/2)^6 = 1/64   The number of possible cases is 6C3 = 20.   P(exactly 3 rainy days) = 20*1/64 = 5/16   The answer is 5/16.
<result>B</result>
If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 9 inclusive?