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    devastation69's Avatar
    devastation69 Posts: 7, Reputation: 1
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    #1

    Oct 21, 2007, 03:44 PM
    probabilty homework on socks.
    Allright this is my question its big... please teach me how to solve it too...

    Sean has a drawer containing 12 black socks, 12 brown socks, 12 blue socks and 12 green socks, all loose and not properly paired. Sean takes socks out of the drawer at random without replacements in the dark. How many socks must Sean take out to ensure that he has a pair of socks of each of the four colors among those he has chosen?
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    #2

    Oct 21, 2007, 03:45 PM
    Quote Originally Posted by devastation69
    Allright this is my question its big... please teach me how to solve it too...

    Sean has a drawer containing 12 black socks, 12 brown socks, 12 blue socks and 12 green socks, all loose and not properly paired. Sean takes socks out of the drawer at random without replacements in the dark. How many socks must Sean take out to ensure that he has a pair of socks of each of the four colors among those he has chosen?
    Yup?
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    Capuchin Posts: 5,255, Reputation: 656
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    #3

    Oct 21, 2007, 03:47 PM
    Well, what's the maximum number of socks you could have without having a pair in all 4 colors? Therefor how many do you need to ensure that you get a pair of each color?
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    devastation69 Posts: 7, Reputation: 1
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    #4

    Oct 21, 2007, 03:48 PM
    Quote Originally Posted by Capuchin
    Well, what's the maximum number of socks you could have without having a pair in all 4 colors? Therefor how many do you need to ensure that you get a pair of each color?
    I'm not sure? Lol I'm real bad at probability... my weak point.
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    devastation69 Posts: 7, Reputation: 1
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    #5

    Oct 21, 2007, 03:50 PM
    I mean I know the probability of getting any sock of any color is 1/4
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    #6

    Oct 21, 2007, 03:54 PM
    And I'm think that the chance of him getting two socks of any color is 1/6 but I'm not sure on how to find the answer.
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    galactus Posts: 2,271, Reputation: 282
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    #7

    Oct 21, 2007, 04:05 PM
    Consider the worst case and worst luck pulling out socks. I pull out 12 green, 12 blue, 12 brown and then 1 black. One more draw and I have my pair of blacks. 38
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    #8

    Oct 21, 2007, 04:09 PM
    So I would go through 38 socks before I get a pair of black socks? Then there is the rest of the socks... but how many socks would I go through before I got a pair of blue, green, or brown socks? Obviously I have them all in my hand. But I don't believe that is the answer to this..
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    galactus Posts: 2,271, Reputation: 282
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    #9

    Oct 21, 2007, 04:12 PM
    38 is the number to be 100% sure of getting one of each color pair. I listed out a worst case scenario. Of course, empirically, you could draw them out and get the required pairs in less draws.
    Why wouldn't that be there answer? Think about it.
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    #10

    Oct 21, 2007, 04:18 PM
    That is true... I'm not replacing the sock... but it feels like there is more to it somehow... can it really be that simple? Lol how would I draw it out?
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