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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 to the original question is 3.

How many would you need to take out to guarantee a pair of Black Socks?

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How many would you need to take out to guarantee a pair of Black Socks?

7.

Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

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How many would you need to take out to guarantee a pair of Black Socks?

7.

Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

A question for you: If the first sock happens to be a white one, and you put it back does the next sock picked count as the 2nd draw, or the 1st? I'm assuming that you mean it to count as the 2nd. And so on....

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How many would you need to take out to guarantee a pair of Black Socks?

7.

Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

A question for you: If the first sock happens to be a white one, and you put it back does the next sock picked count as the 2nd draw, or the 1st? I'm assuming that you mean it to count as the 2nd. And so on....

Yup, that is correct.. infact there is an obviously logical method to do this.. but as most discovered is obvious after discovered

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3 ?

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Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw <!-- s:mrgreen: --><!-- s:mrgreen: -->

First I thought this was a negative binomial problem, then a hyper geometric problem, but it's been a while since stat and I don't know if it's either.

having a pair by the 5th draw:

77.4%

having a pair by the 10th draw:

98.3%

having a pair by the 50th draw:

virtually 100%

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By Jove, I think I've got it, though Mdsl seems to have posted a response too. Before I read his, I'll submit mine....

The chances of getting a black pair "in" any of the mentioned draws is 1:4.5

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Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

Ok, lets look at it this way (for clarity am stating the whole problem again..)

A drawer has 5 black and 5 white socks. Your task is to pick a black pair, HOWEVER on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw...

Solution approach for a black pair on 2nd draw...

=To get a black pair on the 2nd draw, both the 1st draw and 2nd draw must be black.

P(getting a black sock on 1st draw) = 1/2

P(getting a black sock on 2nd draw) = 4/9 (Since 1st sock was black it is not replaced leaving 4 black socks of total 9)

So, the probability of getting a black pair on 2nd draw is 1/2 * 4/9 = 2/9.

Similarly for getting a black pair on 3rd draw:

1) One of the 1st 2 picks have to be black - probability of either 1st OR 2nd resulting in black sock AND

2) 3rd draw must be black..

so y'all get the idea, try to figure a general formula..

And, since it is a probability question, the answer will have to be between 0 and 1 (both inclusive).

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Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

Ok, lets look at it this way (for clarity am stating the whole problem again..)

A drawer has 5 black and 5 white socks. Your task is to pick a black pair, HOWEVER on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw...

Solution approach for a black pair on 2nd draw...

To get a black pair on the 2nd draw, both the 1st draw and 2nd draw must be black.

P(getting a black sock on 1st draw) = 1/2

P(getting a black sock on 2nd draw) = 4/9 (Since 1st sock was black it is not replaced leaving 4 black socks of total 9)

So, the probability of getting a black pair on 2nd draw is 1/2 * 4/9 = 2/9.

Similarly for getting a black pair on 3rd draw:

1) One of the 1st 2 picks have to be black - probability of either 1st OR 2nd resulting in black sock AND

2) 3rd draw must be black..

so y'all get the idea, try to figure a general formula..

And, since it is a probability question, the answer will have to be between 0 and 1 (both inclusive).

My solution was to figure out the probability of NOT drawing a pair of black and subtracting that number from one (or 100%). For 5 draws, person has a 1 in 32 chance of drawing all white socks (1/2^5). there are 5 ways you can draw 1 black sock, each having a different probability: draw 4 W then 1 B, 1/32. draw 3 W, 1 B, 1 W 5/144 because the odds of drawing the last W is 5/9 while the other socks had a probability of 1/2. So any white socks drawn after a black has a p of 5/9 since the black sock was not replaced. Subtracting the p of each situation from 1 gave me my answers (rounded and given as percents).

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Your task is to pick a black pair, on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw

Ok, lets look at it this way (for clarity am stating the whole problem again..)

A drawer has 5 black and 5 white socks. Your task is to pick a black pair, HOWEVER on removing a sock you are supposed to put it back if its not black. What is the probability of having a black pair in the 5th draw, 10th draw, 50th draw...

Solution approach for a black pair on 2nd draw...

To get a black pair on the 2nd draw, both the 1st draw and 2nd draw must be black.

P(getting a black sock on 1st draw) = 1/2

P(getting a black sock on 2nd draw) = 4/9 (Since 1st sock was black it is not replaced leaving 4 black socks of total 9)

So, the probability of getting a black pair on 2nd draw is 1/2 * 4/9 = 2/9.

Similarly for getting a black pair on 3rd draw:

1) One of the 1st 2 picks have to be black - probability of either 1st OR 2nd resulting in black sock AND

2) 3rd draw must be black..

so y'all get the idea, try to figure a general formula..

And, since it is a probability question, the answer will have to be between 0 and 1 (both inclusive).

That's about what I did to get my answer above. 1:4.5 could have read 2/9. The probablility is once in wvery 4.5 draws.

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If there are five black socks in the drawer along with five white socks, this means you probable have one of each color already.

In this case, you would only need one sock.

If you are married to someone similar to my wife, the missing socks are probably left at the laundry mat; therefore, you would need to pull three socks.

In the land of the one legged men the two legged man is king; socks come in pair.

Edited by fredred
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If you are able to distinguish between white and black then this question becomes a little pointless.

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I think I get what jkyle is saying

if you can tell when you pull out a black sock, in order to immediately put it back

but you can't tell what color it is when it's in the drawer... well...

socks to be you!!!!

man, I'm clever

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It says the minimum to be sure you have a pair.

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Dekk, it seems you didn't read all of the posts on this topic. The original question says that there are 5 black socks and 5 white socks in a drawer. Drawing at random or with your eyes closed or with the lights out or however, how many socks must you pull to guarentee a pair? It was established very quickly that the answer would be three. Worst case scenario: You pull one of each color on the first two draws, the third will have to match one of them. Then someone asked what the odds would be if you tried to pull out a certain colored pair (white or black, I can't remember) but put a pulled sock back if it was the wrong color. So I say, if you can tell what color it is, then it pretty much defeats the entire drawing at random theme.

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Ok, so I think you guys are making it way more difficult than it should be. I'm looking at it from a brain-teaser perspective, not a math problem.

So my answer is 2 because the puzzle says you need matching socks, but then when it asks the question it doesn't specify that you're trying to get a match. It just says "What's the minimum number of socks you need to draw to make a pair?" And that answer is simple, 2.

That's my 2 cents worth.

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The answer to the original question is 3.

How many would you need to take out to guarantee a pair of Black Socks?

6

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I thought you just needed two of the same color. If you only have two colors to chose from, ie. black and white, then you will need a total of three draws. This is assuming you pulled a black and a white on your first two draws, in which case you would need only a third draw to match up either a black pair or a white pair. On the other hand, if you are lucky, you might just pull out two black socks, or two white socks on your first two tries, which depletes the purpose of a third draw.

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The minimum draws is 2... if you get lucky, 3 if you want to guarantee a pair.

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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?

2 socks. doesnt say it has to be the same colour, 2 of anything makes a pair

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2 socks. doesnt say it has to be the same colour, 2 of anything makes a pair

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?

Seven, the OP clearly stated the pair should be of the same color.

2 if you are lucky, and 3 to guarantee you have a pair of the same color.

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3 socks.if the first two don't match the third will with one of them.

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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?

3

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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.

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