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Who needs socks?

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by gmat6087 » Mon Oct 29, 2012 5:01 pm
1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1

OA E
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by aneesh.kg » Mon Oct 29, 2012 11:31 pm
gmat6087 wrote:1. There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four socks are picked at random what is the probability of getting two socks of the same color?
A. 1/5
B. 2/5
C. 3/4
D. 4/5
E. 1

OA E
If you pick 4 socks from these 20 socks, you are bound to have atleast one pair (or two socks) of socks of the same colour.
e.g. WWBG, WBBG, WBGG, WWGG, etc.

Think of a possibility where all the four socks are of different colours?
You can't. Because there are just three colours avavilable, you'll have to repeat atleast one of them.

Thus, required probability = 1
Aneesh Bangia
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by abhi131 » Wed Oct 31, 2012 5:48 pm
Agree with the answer above.
This is how I look at it.
Let's say the first three socked picked come out to be different colors. Regardless of what color sock comes out last, there will already be one that matches. Hence, probability will be 1.
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