A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 7 hats randomly out of the drawer and returning each hat before taking out the next one?  Choose the most appropriate option.
A) 3/4	B) 5/8	C) 9/16	D) 17/32	E) 35/64
Let's find the probability of getting exactly 3 red hats.   One possible case is red-red-red-blue-blue-blue-blue.   The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/128   There are 7C3 = 35 such cases so we need to multiply this by 35.   P(exactly 3 red hats) = 35*1/128 = 35/128   Clearly the probability of getting exactly 3 blue hats will also be 35/128.   The sum of the probabilities is 35/128+35/128 = 70/128 = 35/64   The answer is 35/64.
<result>E</result>
A drawer holds 5 red hats and 5 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 7 hats randomly out of the drawer and returning each hat before taking out the next one?