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 10 inclusive?
Choose the most appropriate option
A) 7/32  B) 11/64  C) 35/128  D) 49/128  E) 65/128
One possible case is: rainy-rainy-rainy-not rainy-not rainy-not rainy-not rainy.   The probability of this case is (1/2)^7 = 1/128   The number of possible cases is 7C3 = 35.   P(exactly 3 rainy days) = 35*1/128 = 35/128   The answer is 35/128.
<result>C</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 10 inclusive?