M26-10

Question

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.  \frac{1}{5}  
B.  \frac{2}{5}  
C.  \frac{3}{4}  
D.  \frac{4}{5}  
E. 1

Bunuel · Accepted Answer

Official Solution:

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.  \frac{1}{5}  
B.  \frac{2}{5}  
C.  \frac{3}{4}  
D.  \frac{4}{5}  
E. 1

No formula is needed to answer this one. The trick here is that we have only 3 different color socks but we pick 4 socks, which ensures that in ANY case we'll have at least one pair of the same color (if 3 socks we pick are of the different color, then the 4th sock must match with either of previously picked one).  P=1 .

Answer: E

spetznaz · Answer

A good tricky one ! +1 kudos

sathishm07 · Answer

Hi,

I can understand the logic behind this. Can anyone solve this using combination??

Thanks,
Sathish

dkrunic · Answer

I initially had 1, but after re-reading the question I interpreted it as getting exactly 2 socks of the same color. What makes this interpretation incorrect? Also, how would you solve if the problem asked for exactly 2 socks of the same color.

dsheth7 · Answer

@ Buenel;

Great Question.

Any Link to understand the nuances of Probability?

Many Thanks.

Bunuel · Answer

Check the links below:

Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability 
 Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.

CPGguyMBA2018 · Answer

I understand the logic of this question, and how the answer has to be 1.
However, shouldn't the answer solving it by combinatorics give the same answer = 1?

For example, shouldn't (10C2)(6C1)(4C1) + (6C2)(10C1)(4C1) + (4C2)(10C1)(6C1) / 20C4 = 1?
When I solved it, it gave me 8/19.

What is wrong with the approach above?

arjittak · Answer

Because you ignored the other possibilities in your formula such as 2 pairs of exactly 2 different color and 2 pairs of same color

Hope this makes it clear

Sent from my A0001 using  GMAT Club Forum mobile app

Bunuel · Answer

Duplicate of M02-06. Unpublished....................

bumpbot · Answer

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M26-10

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