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There are 5 pairs of white, 3 pairs of black

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by conquistador » Mon Oct 12, 2015 3:31 pm
Source: Gmatclub

There are 5 pairs of white, 3 pairs of black and 2 pairs of grey socks in a drawer. If four individual socks are picked at random what is the probability of getting at least two socks of the same color?

A. 15
B. 25
C. 1
D. 35
E. 45

naturally in all the probability and combinations problems, a condition with or without replacement is mentioned which plays a key role in deciding the answer.

Isn't the same missing here? Explain.
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by [email protected] » Mon Oct 12, 2015 3:54 pm
Hi Mechmeera,

This looks like someone took a 'worst-case scenario' question and designed it in 'reverse.'

Since each of the three colors has at least 2 socks in that color, the probability of getting at least one matching pair is 100%. Here's why...

IF....your first 3 socks were one of each color:

1 white, 1 black and 1 grey.....

Then the 4th sock would automatically match one of the prior 3, so you'd have a matching pair no matter what. In the realm of probability math, a 100% probability is written as 1/1 = 1.

Final Answer: C

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by conquistador » Mon Oct 12, 2015 4:40 pm
[email protected] wrote:Hi Mechmeera,

This looks like someone took a 'worst-case scenario' question and designed it in 'reverse.'

Since each of the three colors has at least 2 socks in that color, the probability of getting at least one matching pair is 100%. Here's why...

IF....your first 3 socks were one of each color:

1 white, 1 black and 1 grey.....

Then the 4th sock would automatically match one of the prior 3, so you'd have a matching pair no matter what. In the realm of probability math, a 100% probability is written as 1/1 = 1.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Yes you are right.
a condition with or without replacement does not matter here.
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by Matt@VeritasPrep » Wed Oct 14, 2015 11:45 pm
This question is a (basic) illustration of something called the Pigeonhole Principle, one of my favorite ideas in math.

It's incredible how often this comes up in higher math, and it's equally incredible that you can use it to prove that there exist two people in New York City who have the exact same number of hairs on their heads! (Check that link if you're interested.)
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