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# A certain ski shop sells pairs of gloves in 12 different colors

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Intern
Joined: 21 Jan 2017
Posts: 33
Re: A certain ski shop sells pairs of gloves in 12 different colors  [#permalink]

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10 Jul 2018, 00:56
Bunuel wrote:
A certain ski shop sells pairs of gloves in 12 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?

A. 1/144
B. 1/143
C. 1/24
D. 1/23
E. 1/12

We have 2*12 = 24 gloves on the floor. After we pick ANY, there are 23 left and there is only 1 matching pair left for the one we've already picked, so P = 1/23.

Or: there are 12 matching pairs, and $$C^2_{24}=23*12$$ ways to pick any two. P = (favorable)/(total) = 12/(23*12) = 1/23.

Hope it's clear.

Hi Bunuel,

why is (24c1 * 1) / 24c2 wrong??
As there are 24 gloves, we need to first pick one glove, so 24c1.
Then we have only one way to pick the other glove, so 1.
Total outcomes=picking two out of 24 = 24c2.

we get 2/23, so where am I going wrong?

Thanks,
Uma
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Re: A certain ski shop sells pairs of gloves in 12 different colors  [#permalink]

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10 Jul 2018, 19:56
Hi Uma,

There are 12 pairs of gloves - and the prompt asks for the probability of pulling out a pair of matching gloves (NOT a "specific" pair of matching gloves). Thus, the first glove selected can be ANY color (and has an equal probability of being any color) and does not impact the overall calculation. It's the SECOND glove that you have to think about - since it has to match the first glove selected. There will only be 1 glove that matches, out the of the 23 gloves remaining, so the probability will be 1/23. If there wasn't an equal probability of pulling each type of glove on the first try, then the math would be different, but that's not the case here.

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Re: A certain ski shop sells pairs of gloves in 12 different colors  [#permalink]

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10 Jul 2018, 23:45
EMPOWERgmatRichC wrote:
Hi Uma,

There are 12 pairs of gloves - and the prompt asks for the probability of pulling out a pair of matching gloves (NOT a "specific" pair of matching gloves). Thus, the first glove selected can be ANY color (and has an equal probability of being any color) and does not impact the overall calculation. It's the SECOND glove that you have to think about - since it has to match the first glove selected. There will only be 1 glove that matches, out the of the 23 gloves remaining, so the probability will be 1/23. If there wasn't an equal probability of pulling each type of glove on the first try, then the math would be different, but that's not the case here.

GMAT assassins aren't born, they're made,
Rich

Ok! Got it. In other words, if they ask you to select a pair from few pairs, we can simply go by this method:
12c1/24c2=1/23.
Re: A certain ski shop sells pairs of gloves in 12 different colors &nbs [#permalink] 10 Jul 2018, 23:45

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