SOLUTION: Amanda and Dirk are renting in‐line skates for a day in the park. They both take the same size shoe, and there are 5 pairs remaining in their size. Unbeknownst to them, 3 of the

Question 1143695: Amanda and Dirk are renting in‐line skates for a day in the park. They both take the same size shoe, and there are 5 pairs remaining in their size. Unbeknownst to them, 3 of the pairs of skates have defective bearings. If they randomly choose 2 pairs, what is the probability they will both get a pair of skates that are not defective?
(Hint: List all of the outcomes of the sample space.)

The probability that they will both get a good pair of s

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777) (Show Source): You can put this solution on YOUR website!
.

The probability that Amanda will randomly select a good pair is . The probability that Dirk will randomly select a good pair (making selection after Amanda) is . The probability that they BOTH will randomly select good pairs is the product P = . = . ANSWER

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P.S. I am not going to list all the pair -- too much work for me . . .

So, I do not need your hint.

I have enough brain cells in my head, instead.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

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.

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.

So here is another basic way of solving this problem.

(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.

The probability that they both select good pairs is then

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