probability

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fizzanasir: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Aug 08, 2011 11:40 pm

by fizzanasir » Fri Dec 16, 2011 2:27 am

In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

Answer is 4

i cant understand the question, what exactly is the question asking for?

Source: Beat The GMAT — Problem Solving | Fri Dec 16, 2011 2:27 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Dec 16, 2011 2:32 am

You have 3 colors of socks - Black, Grey and Orange. (forget the number of pairs)

If you're picking up socks randomly, what is the minimum number you need to pick up to ensure you get at least one pair (of same color)

Assuming worst scenario where the first 3 are all of different colors, the 4th sock you pick up will definitely be a pair with anyone of the first three.

ankush123251: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu Feb 17, 2011 1:36 amFollowed by: 2 members; Thanked: 8 times

by ankush123251 » Fri Dec 16, 2011 2:36 am

Hi fizzanasir,

Firstly i believe this is not a probability question but a logic question.
To solve this just frame it like this:
# of Black socks = 8,# of Gray = 6 and # of Orange Socks = 4.
Now first three picks of sock can be of different colors Black/Grey/Orange.So to ensure Scoks of same color removed you will require one more pick.Thus 4 socks must be removed.

safin: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Sep 20, 2015 7:48 pm

by safin » Sun Sep 20, 2015 7:50 pm

the part i dont understand is that you could pick two socks or even three socks of the same color. the question mention the word random. so there is no order here. so you could pick up 2/3 socks of the same color. please help

mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Sun Sep 20, 2015 10:57 pm

I see what you are saying. You are thinking what if the first two socks themselves were of the same color. You are thinking of the probability of different cases. I think the word 'random' has been used to mislead us a little. I realised not immediately that the question is not about probability at all. It is just asking what is the minimum number of socks that should be removed to ensure that two socks of the same color will have been removed. I guess removing four socks is a way of 'ensuring' that two same color socks will have been removed...

Experts could comment on this further.

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by [email protected] » Mon Sep 21, 2015 9:03 am

Hi All,

The concept in these types of questions is based on the 'worst case scenario' - to guarantee that something will happen, you have to focus on the 'extreme/longest' way that it could happen.

Here, we have 8 black socks, 6 gray socks and 4 orange socks. The question asks for the MINIMUM number of socks that would be need to be randomly removed from the drawer to guarantee that a matching pair of socks would drawn. Since the original poster didn't include the 5 answer choices, we're forced to deal with this prompt in a certain way (instead of using the answers to our advantage).

So let's start with 2 socks - is it possible that you could draw 2 socks and NOT get a matching pair? Certainly - there are several examples. If we pull one black sock and one gray sock, then we do NOT have a matching pair. Thus, 2 socks is NOT enough to guarantee a matching pair.

Next, let's try 3 socks - is it possible that you could draw 3 socks and NOT get a matching pair? Absolutely - if we pull one black sock, one gray sock and one orange sock, then we do NOT have a matching pair. Thus, 3 socks is NOT enough to guarantee a matching pair.

Next, let's try 4 socks - is it possible that you could draw 4 socks and NOT get a matching pair? NO, and here's why - if we pull one black sock, one gray sock and one orange sock....we would still have to draw one more sock - and that 4th sock would match one of the 3 colors that we had already pulled. So we WOULD have a matching pair and 4 socks IS enough to guarantee a matching pair.

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by Matt@VeritasPrep » Thu Sep 24, 2015 10:24 am

mindful wrote:I see what you are saying. You are thinking what if the first two socks themselves were of the same color. You are thinking of the probability of different cases. I think the word 'random' has been used to mislead us a little. I realised not immediately that the question is not about probability at all. It is just asking what is the minimum number of socks that should be removed to ensure that two socks of the same color will have been removed. I guess removing four socks is a way of 'ensuring' that two same color socks will have been removed...

Experts could comment on this further.

The key here is that the question wants the probability of getting two socks that match, not two socks of a SPECIFIC COLOR that match.

For instance, if I gave you a bucket with two red marbles, two green marbles, and two blue marbles, and asked you to pull out two marbles at random, your probability of getting ANY two of a kind is going to be much higher than your probability of getting two blue marbles, since there are more ways in which you could do so.

mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Tue Sep 29, 2015 11:36 pm

Thanks Rich for the detailed explanation.

Thanks Matt for this nuance.

Interesting point. But the question asks only ", what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed? "

It actually does not ask for probability. However, are you suggesting that the probability of picking any two socks of the same color is actually going to be 4? (Probabilities can actually be greater than 1? I thought this wasn't possible. If so, do you mind showing what the numbers or the math would look like?)

mindful: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Wed Jun 24, 2015 10:57 pmFollowed by: 1 member; Thanked: 3 times

by mindful » Tue Sep 29, 2015 11:36 pm

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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:11 pm

fizzanasir wrote:In a certain sock drawer, there are 4 pairs of black socks, 3 pairs of gray socks and 2 pairs of orange socks. If socks are removed at random without replacement, what is the minimum number of socks that must be removed in order to ensure that two socks of the same color have been removed?

Answer is 4

We can remove 1 black, 1 gray, and 1 orange sock first. The next sock selection of any color would ensure that at least one pair of socks of the same color has been removed. Thus, 4 socks would have to be removed.

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