Question 1201706
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A student just learning about probability should be able to solve this problem by both of two basic probability methods.<br>
(1) Pick one shirt at a time....<br>
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.<br>
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.<br>
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.<br>
ANSWER: (5/8)(4/7) = 20/56 = 5/14<br>
(2) Using "n choose r"....<br>
The number of ways of choosing any 2 of the 8 shirts is "8 choose 2": {{{C(8,2)=(8*7)/(2*1)=28}}}<br>
The number of ways of choosing 2 of the 5 short-sleeve shirts is "5 choose 2: {{{C(5,2)=(5*4)/(2*1)=10}}}<br>
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<br>
ANSWER: (again, of course...) 5/14<br>