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# In packing for a trip, Sarah puts three pairs of socks - one

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Senior Manager
Joined: 03 Apr 2013
Posts: 292

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Location: India
Concentration: Marketing, Finance
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Re: In packing for a trip, Sarah puts three pairs of socks - one [#permalink]

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03 Jul 2017, 01:32
Bunuel wrote:
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!

$$\frac{C^2_3}{C^2_6}=\frac{3}{15}=\frac{1}{5}$$: $$C^2_3$$ = picking 2 pairs out of 3 and $$C^2_6$$ = picking 2 socks out of 6.

Bunuel
Aren't any socks of the same color identical?
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Manager
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In packing for a trip, Sarah puts three pairs of socks - one [#permalink]

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29 Jul 2017, 09:41
Bunuel wrote:
akhil911 wrote:
In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?

A. 1/5
B. 1/4
C. 1/3
D. 2/3
E. 4/5

I have not understood how to solve this question properly , can someone help me out here.
Kudos me if you like the post !!!

$$\frac{C^2_3}{C^2_6}=\frac{3}{15}=\frac{1}{5}$$: $$C^2_3$$ = picking 2 pairs out of 3 and $$C^2_6$$ = picking 2 socks out of 6.

Why are you choose formulas upside down. I have never seen it presented in the other way. Also, it seems a little odds that we can use two different formulas to calculate the answer. 2 pairs out of 3 divided by individual socks.

I like the OA explanation better that of the 2 remaining socks not taken we have 1 sock that could be any color. And given it is red, blue or green what is the odds the other one is red blue or green.

What is the odds that this matches. So we know there are 6 stocks so 1/5 socks remain to match it. Or 1/5 match. And if the pair not chosen matches that means the other 2 also match. And as mentioned, I have always seen $$C^3_2$$

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Re: In packing for a trip, Sarah puts three pairs of socks - one [#permalink]

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07 Dec 2017, 14:44
Hi All,

In probability questions, there are only 2 things that you can calculate: what you WANT and what you DON'T WANT.

(WANT) + (DON'T WANT) = 1

In this question, we can calculate the probability of what we DON'T WANT and subtract it from 1 to figure out the probability of what we do WANT.

The question asks for the probability of pulling 4 socks out that form 2 matching pairs. For this to occur, the two socks that are left would also form a matching pair. If the 2 leftover socks DO NOT form a matching pair, then the 4 socks that are pulled will NOT form 2 matching pairs.

Probability of 2 socks NOT forming a matching pair…

1st sock = 1 (any of the socks can be the first sock)
2nd sock = 4/5 (since there's only one sock that matches the first sock).

Probability of NOT forming a pair with 2 socks: = 1 x 4/5 = 4/5 (which ALSO means a 4/5 chance of NOT having 2 matching pairs of 2 socks)

1 - 4/5 = 1/5 (meaning a 1/5 chance of having 2 matching pairs of 2 socks).

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A

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Re: In packing for a trip, Sarah puts three pairs of socks - one   [#permalink] 07 Dec 2017, 14:44

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