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# socks

## Question

You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

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The answer is 2 if you don't need the pair to match (it just says a pair). Or 6 if you need to assure a matching pair.

The answer to the subsequent post about probability on the nth draw of having a pair is integral approaching 100%. In other words as the number of draws in creases the chances of getting the pair increases. The formula is 2n/9 I got that because your first draw is always 1/2 and any subsequent draw has a probability of 4/9's for the black sock. the answer is 1/2*4/9 times the summation of 4^n/9^n where n goes from 2 to infinity. If I could make the math chars here I would have... properly reduced that equals

2/9 + E4^n/9^n

again where n starts at 2 and goes to infinity... E = sigma. I am pretty sure thats right my last calc course a few years ago but that should do it. I use the summation because the probabilities of each draw must add together to get the total probability at infinity draws it equals 100% or 1.

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The question, as stated by another poster, does NOT say to 'guarantee' you have a pair...read again....therefore the minimum MAY be 2 if you happen to choose two of the same color in draws 1 and 2....and thus 3 draws to GUARANTEE a matching pair of either color

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2 socks they are all black in the dark..

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2 obviously but 3 for a pair and 6 for a black/white pair

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2, for a pair = 2. OBVIOUSNESS!!!!

The End.

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In a pair, there are two socks. So, the minimum # of socks you have take out is 2, that could give you two matching. The maximum is 3, because if after the first 2 draws, you get two different ones, than you can just draw one more to match with one of the 2.

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The minimum number of socks you need to take out in order to make a pair is 2. You just need to be able to feel the differences between them. When one of your senses is disabled you adapt, each brand of sock is going to have its own unique texture, so it is possible to reach in and come up with the matching pair on your first try.

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The answer is 2 if you don't need the pair to match (it just says a pair). Or 6 if you need to assure a matching pair.

Not quite. You need 7 socks to guarantee a black pair. This is assuming that you don't put a sock back when it is white. If you do put a sock back if it is white, then you will need an infinite number of draws to guarantee a black pair.

Plus, it clearly says a pair of the same color.

Edited by Noct
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Here is how I see it. The minumum number is two. Of course, you have to be lucky to get either 2 white or two black socks but whichever you are going for, the minimum you could do in is two - if you are lucky.

Now if you are unlucky and you were going for either a pair of white or black socks, you could try 5 times and not get it since all five could be the wrong color. That means the maximum number that you would have to pull is six to get a pair of a particular color - if you are unlucky.

It seems to me that anything inbetween is purely conjecture. Is anything wrong with this logic?

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Here is how I see it. The minumum number is two. Of course, you have to be lucky to get either 2 white or two black socks but whichever you are going for, the minimum you could do in is two - if you are lucky.

Now if you are unlucky and you were going for either a pair of white or black socks, you could try 5 times and not get it since all five could be the wrong color. That means the maximum number that you would have to pull is six to get a pair of a particular color - if you are unlucky.

It seems to me that anything inbetween is purely conjecture. Is anything wrong with this logic?

You stated that I could be extremely unlucky and pull out 5 black ones in a row. Then say that the maximum needed is 6 to get a pair of a specific color.

So if I want to get a pair of white socks. I'm extremely unlucky and pull out 5 black socks in a row. And then I pull out a white sock. So I've pulled out 6 socks, but still don't have a white pair.

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You stated that I could be extremely unlucky and pull out 5 black ones in a row. Then say that the maximum needed is 6 to get a pair of a specific color.

So if I want to get a pair of white socks. I'm extremely unlucky and pull out 5 black socks in a row. And then I pull out a white sock. So I've pulled out 6 socks, but still don't have a white pair.

That is correct, I agree. If you are extremely unlucky it you might have to pull a sock 7 times to get a pair of the color you want. Actually, if had to do it I would just grab as many as I could, probably all of them, select the desired pair and return the rest to their place in the dark.

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You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

The answer to this question is NOT 3, it's 2. 3 is the minimum number to GUARANTEE two socks of the same color. But the minimum number to make a pair is always 2.

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You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

Actually if you want to get technical and most people on here do. The correct answer would be simply 2. The question asks what is the minimum number of socks needed to make a pair. It does not specify that they need to be like colors

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Actually if you want to get technical and most people on here do. The correct answer would be simply 2. The question asks what is the minimum number of socks needed to make a pair. It does not specify that they need to be like colors

the very first post states "You are in the dark and you need to make a pair of the same color to wear" why do people keep saying that the original post doesnt say that the colors must match, clearly......IT DOES.

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You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

the answer is 2. there is no other possible answer. you might get lucky and the first 2 you pull out will match in color. therefore the "minimun" is set at 2.

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Lol, its too, if you're lucky.

That was easy.

However some people don't pay attention and don't get it.

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The answer is two. You did not say a matching pair.

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Answer #1: Since the question doesn't state minimum number required to guarantee a pair, the answer is Two. You could get lucky and draw a match with the first two.

Answer #2: If you want to guarantee a pair of socks, the answer is Three.

Answer #3: If you want to guarantee a specific color of socks, the answer is Seven.

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You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

you have to take 3 for maiking a pair and 7 to make a color you wish (for 100% probability)

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y cant people just organize there socks?!?!?!?!?!??!?

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3 ?

thank you thats the exact answer i was thinking i have no idea where these guys are getting 7???

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You have a drawer where you mixed 5 black socks and 5 white socks. You are in the dark and you need to make a pair of the same color to wear. What is the minimum number of socks you need to take out in order to make a pair?

I hate to be a party pooper or to be accused of pedanticism, but:

The MINIMUM number of socks needed to make a pair is 2. Admittedly the probability of drawing a matched pair is not 100%, but that was not part of the stated problem.

To GUARANTEE a matched pair, the answer 3 is correct. The proper wording might be reworded to "What is the minimum number of socks you need to draw to make sure you have a pair of matched socks."

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The correct answer is to just wear sandals. Then die because you realize you accidentally put on mismatching socks before you put the sandals on.

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