A drawer holds 5 red hats and 5 blue hats.
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 4 hats randomly out of the drawer and returning each hat before taking out the next one?
Answer/Solution
1/2
Steps/Work
Let's find the probability of getting exactly 3 red hats.
One possible case is red-red-red-blue.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we need to multiply this by 4.
P(exactly 3 red hats) = 4*1/16 = 1/4
Clearly the probability of getting exactly 3 blue hats will also be 1/4.
The sum of the probabilities is 1/4+1/4 = 1/2
The answer is C.
One possible case is red-red-red-blue.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we need to multiply this by 4.
P(exactly 3 red hats) = 4*1/16 = 1/4
Clearly the probability of getting exactly 3 blue hats will also be 1/4.
The sum of the probabilities is 1/4+1/4 = 1/2
The answer is C.