Question 1143695
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Tutor @ikleyn showed one method for solving this problem by finding the probability that the first person selects a good pair (2 out of 5) and then the second person selects the other good pair from the pairs that are left (1 out of 4).  Then the probability that they both pick good pairs is (2/5)*(1/4) = 2/20 = 1/10.<br>
It is always good to know more than one way to solve a problem.  For me, with problems in probability in particular, I like to be able to solve a problem by two different methods and get the same answer; it gives me reassurance that my analysis of the problem and my methods of solution are correct.<br>
So here is another basic way of solving this problem.<br>
(1) The two people have to select both of the 2 good pairs: 2 choose 2.
(2) The number of different ways they can select 2 of the 5 pairs is 5 choose 2.<br>
The probability that they both select good pairs is then<br>
{{{C(2,2)/C(5,2) = 1/10}}}