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Badri has 9 pairs of dark Blue socks and 9 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?

(1) (2*9C2 * 9C1) / 18C3 (2) (9C2 * 9C1) / 18C3
(3) 1 (4) None of these

Correct Answer - (3)

This problem has been seen in the Question Bank the Ascent website.

You will notice that Badri will fail to find a matching pair in two situations which are:

1) The picks are all of one side either Left or Right. This happens in 2*18C3 ways.
2)Two picks of same side and color and one of another side and color. This happens in 4*9C2*9C1 ways.

Both these account for 2928 ways.

The corect answer, in my opinion is (4).

This is an interesting problem with practical significance as its inconvenient many a times to pick a matching pair when socks are packed randomnly in the same bag.

Shaji.

Hi all
Iam not sure but I think the answer should be 1.
This is because u will always end up picking up atleast 2 socks of the same color when we have to pick 3 socks in total.
eg. dark blue, black (third can be either dark blue or black)
So we end up pickin up a pair of same color

But then again the socks that are picked up can be of the same leg as Shaji has pointed out..
If anybody has anythin to add then please do..

Regards
Himanshu

Hi;
Picking up a pair of the same color wouldn't necessarily make a matching pair as you can notice from my explanation.

Regards;

Shaji

This is indeed an interesting question.
Another practical implication of the question is that the right solution depends on which assumption we apply, because the question does not say exactly what "matching pairs" means.
I would have implied the assumption that "matching pairs" means "matching colours" in this context, - because no other factors have been mentioned in the question - but Shaji's solution suggests otherwise. In Shaji's solution we need to assume external factors beyond those given in the question itself, and one would not know with certainity in which cases it is justified to do so.
Since this kind of dilllemma is not unusual, it would be a great help if someone could provide a GMAT-specific guidelines on which assumption to apply on the test when in doubt like this.

Hi;

The only point there is no dillemma about is that the problem is interesting.

Having agreed on that, the bizzarre assumption that a matching pair implies that they be of the same color takes out all the interest out of the question making it very trivial.

Nevertheless, option 4 makes it very explicit on what a matching pair is meant by the question setterand obviously the socks do not become a matching pair unless and otherwise they are of the same color and of two different sides.


GMAT question setters are notorious for sneaking in some 'dillemma' or a catch for the naive test-taker. But quite frankly, this question is far from it.

Regards;

Shaji.

Hi Shaji:)

Thanks a lot for your reply.
I do understand your logic that leads to the assumption that option 4 is the right solution, but this is exactly what my doubts are about: if you would be a test taker on a live test, your brilliance may not be rewarded by being acknowledged for having found the right answer; ONLY if it so happens that the question setter had the very same in mind.
(Please note that the question is about socks rather than shoes)

My argument in detail:
My main point is that on an objective level such a doubt cannot be resolved. Merely considering the level of difficulty of a question if a certain answer is applied, or the fact that "None of the above" is among the options, does not make it "explicit" what the test writer has in mind. In many cases the "None" options or too easy questions are only there to distract the test taker. Or, nothing can rule out the possibility that this question with answer 3) is offered on the test from the pool of low level questions.
More importantly, even if the question setter intends to hide the subjective idea of different right and left legs of socks behind option 4, it is not even on an implicit level of expression; it's only in her/his mind. And this is exactly what I am arguing with: the lack of explicitness in a question, when it is definitely needed in order to be able to find THE right answer.
Any meaning of "matching pair" beyond "matching colours" in this context is a very subjective assumption. (B/c the question is about socks, not shoes)

Finally, I don't see the point in building an extra test in a math question like this, that is to test how many justified or far-fetched external factors one can consider within several seconds, and how good s/he is at guesswork when deciding if the test maker meant something else/more by "matching pair" or s/he merely wanted to play a trick with a too easy question and to test the level of the certainty of the test taker in still choosing the trivial yet the correct answer.

Again, thanks for your reply. I do not mean to be being "difficult" with my argument. My doubts are real and it would be beneficial for all if all these angles would be considered by the test writers.
Regards,
eam

Hi Eam;

Thanks for the clarification on your doubt and its real.
Let me now explain the matter more explicitly.

Matching & pair are the keywords. Like shoes,if the socks r of different sides, then they don't form a pair and if the colors aren't same,they don't match. Try wearing socks of the wrong side !!!. They don't fit.
Further, a quote from my earlier post. "This is an interesting problem with practical significance as its inconvenient many a times to pick a matching pair when socks are packed randomnly in the same bag."

On the GMAT trivial answers are usually wrong.

Shaji.

Hi Eam;

Thanks indeed for the posts and the explainations.
U R CORRECT!!!

Indeed, socks are interchangable and surely, three picks would result in a matching pair and the correct answer is option (3) whichis 1.

I"am sure that the ETS answer would also be 1. Consistent use of the same socks on one leg makes it take the profile of thereby its indentity. For GMAT purposes, this is an extraneous assumption.

I'am really sorry for the confusion.

Regards;

Shaji.

Hi Shaji:
Thanks a lot for your thoughts and for the clarification!
Regards,
eam

Hi Guys,

Its superb logic.... I havent thought of it at all.

3 picks from 2 sets will obviously make a pair...




BestRegards
Vishal