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 6 hats randomly out of the drawer and returning each hat before taking out the next one? Answers:
A) 3/8  B) 1/4  C) 5/8  D) 5/16  E) 7/16
Let's find the probability of getting exactly 3 red hats.   One possible case is red-red-red-blue-blue-blue.   The probability of this is 1/2*1/2*1/2*1/2*1/2*1/2 = 1/64   There are 6C3 = 20 such cases so we need to multiply this by 20.   P(exactly 3 red hats) = 20*1/64 = 5/16   Note that when we get exactly 3 red hats, then we also get exactly 3 blue hats.   So we don't need to consider the case of exactly 3 blue hats separately.   The answer is 5/16.
<result>D</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 6 hats randomly out of the drawer and returning each hat before taking out the next one?