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Probability question

by bubbliiiiiiii » Mon Mar 28, 2011 6:37 am
A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

1/190
1/20
1/19
1/10
1/9

OA C

Why not B?

The probability of selecting first shoe from the 20 shoes is 1/20 and then selecting the second one is 1 since it has to be the same shoe!! Please correct me.
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Pranay
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by GMATGuruNY » Mon Mar 28, 2011 6:45 am
bubbliiiiiiii wrote:A box contains 10 pairs of shoes (20 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

1/190
1/20
1/19
1/10
1/9

OA C

Why not B?

The probability of selecting first shoe from the 20 shoes is 1/20 and then selecting the second one is 1 since it has to be the same shoe!! Please correct me.
The first shoe chosen is irrelevant. Since any of the 20 shoes can be chosen, the probability is 20/20 = 1.

The issue at hand is the second shoe. The second shoe chosen must match the first shoe.
Once the first shoe has been chosen, 19 shoes remain. Of these 19 shoes, only 1 will match the first shoe chosen.
Thus, P(matching shoe) = 1/19.

The correct answer is C.

Another approach:
Number of pairs that can be formed from the 20 shoes = 20C2 = 190.
Number of matching pairs = 10.
P(matching pair) = 10/190 = 1/19.
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by bubbliiiiiiii » Tue Mar 29, 2011 2:01 am
Thanks .. GMATGuru!

Can you also suggest few additional resources for following the Quant stuff?
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Pranay
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