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 8 hats randomly out of the drawer and returning each hat before taking out the next one?	Select the correct option:
A) 3/4
B) 5/8
C) 7/16
D) 15/32
E) 31/64
Let's find the probability of getting exactly 3 red hats.   One possible case is red-red-red-blue-blue-blue-blue-blue.   The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2 = 1/256   There are 8C3 = 56 such cases so we need to multiply this by 56.   P(exactly 3 red hats) = 56*1/256 = 7/32   Clearly the probability of getting exactly 3 blue hats will also be 7/32.   The sum of the probabilities is 7/32+7/32 = 14/32 = 7/16   The answer is 7/16.
<result>C</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 8 hats randomly out of the drawer and returning each hat before taking out the next one?