SOLUTION: A closet contains 5 short-sleeve shirts and 3 long-sleeve shirts. Two shirts are chosen from the closet without looking. What is the probability that both shirts have short sleeves
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Question 1201706: A closet contains 5 short-sleeve shirts and 3 long-sleeve shirts. Two shirts are chosen from the closet without looking. What is the probability that both shirts have short sleeves? Found 2 solutions by greenestamps, mananth:Answer by greenestamps(13200) (Show Source):
A student just learning about probability should be able to solve this problem by both of two basic probability methods.
(1) Pick one shirt at a time....
When picking the first shirt, there are 8 shirts, of which 5 are short sleeve. The probability of getting a short-sleeve shirt on the first pick is 5/8.
When picking the second shirt, there are 7 shirts left, of which 4 are short sleeve. The probability of getting a short-sleeve shirt on the first pick is 4/7.
The problem asks for the probability that the first shirt is short-sleeve AND the second shirt is short-sleeve. The "AND" means the two probabilities must be multiplied to get the answer.
ANSWER: (5/8)(4/7) = 20/56 = 5/14
(2) Using "n choose r"....
The number of ways of choosing any 2 of the 8 shirts is "8 choose 2":
The number of ways of choosing 2 of the 5 short-sleeve shirts is "5 choose 2:
The probability of getting two short-sleeve shirts is the number of ways of getting 2 short-sleeve shirts, divided by the total number of ways of choosing 2 of the 8 shirts: 10/28 = 5/14
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Let P be the event a short-sleeve shirt is drawn first.
Let Q be the event a short-sleeve shirt is drawn next.
without replacement, therefore, the sample space decreases after event P
The joint probability is
P(PandQ)=P(Q)P(Q|P)=
