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Math Help - socks in a drawer probability

  1. #1
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    socks in a drawer probability

    I need some help with the following problem:

    You have 30 socks in a drawer, 10 red, 16 black and 4 blue. You are
    removing socks from the drawer in the dark, so you cannot see the colours. How many socks do you need to take out to be certain you have:

    (a) A matching pair of socks.
    (b) Two matching pairs of socks.
    (c) Two matching pairs of different colours.
    (d) Two blue socks.

    My attempt:

    (a) The socks come in three possible colours. If we take one color of eeach sock, then take one more we will have at leasr 1 pair of 1 color: 3+1=4

    (b) We must repeat process in (a) twice: 4+4=8

    (c) If the first 16 we take all happen to be black and the next may 10 happen to be red so we have two matching pairs: 26 socks needed

    (d) I think once all the blacks and reds are gone, we only need to take 2 more which will inevitibly be blue: 10+16+2=28.

    I have a test so I appreciate it if anyone could please correct me.
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  2. #2
    Member Traveller's Avatar
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    a) is alright.

    As for b), suppose we have 3 socks of different colours. We add a sock of some colour to obtain a pair. Now if we add a sock of some different colour then we have two pairs. But if the new sock happens to be of the same colour as the previous one, then it has to be matched with yet another of the same colour. So the answer will be 4+1+1=6.

    c) The first 16 socks can be black. Then we need to pick 3 more socks to get another matching pair. So we have 16+3 = 19

    d) is correct.
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  3. #3
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    Hello, demode!

    You have 30 socks in a drawer, 10 red, 16 black and 4 blue.
    You are removing socks from the drawer in the dark, so you cannot see the colors.
    How many socks do you need to take out to be certain you have:

    \text{(a) A matching pair of socks.}

    Your answer is correct.

    Think of the "worst case scenario".

    You draw 3 socks and get 1 red, 1 black and 1 blue . . . no matching pair.

    The next sock must match one of the three.

    The answer is: 4 socks.



    \text{(b) Two matching pairs of socks.}

    "Worst case": .You draw 3 red, 3 black and 3 blue.
    . . . . . . . . . . .You do not have two matching pairs.

    The next sock must form two pairs of matching socks.

    Answer: .10 socks.



    \text{(c) Two matching pairs of }di\!f\!f\!erent\text{ colors.}

    "Worst case": .You draw all 16 black socks, 1 red sock and 1 blue sock.
    . . . . . . . . . . .You do not have two matching pairs of different colors.

    The next sock (red or blue) must form two pairs of different colors.

    Answer: .19 socks.



    \text{(d) Two blue socks.}

    Your answer is correct.

    "Worst case": .You draw all 10 red socks, all 16 black socks, and 1 blue sock.
    . . . . . . . . . . .You do not have two blue socks.

    The next sock (blue) will gives us a two blue socks.

    Answer: .28 socks.
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  4. #4
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    [Quote]
    "Worst case": .You draw 3 red, 3 black and 3 blue.
    . . . . . . . . . . .You do not have two matching pairs.

    The next sock must form two pairs of matching socks.

    Answer: .10 socks.
    [End Quote]

    I dont know how to do quote. hehe.
    in the question above, it does not state whether you need 2 pairs of the same colour, or two different colours, so the right answer is not 10. If you have 3 different colours, and you need 1 pair, as in part a) the answer would be four. 3 different colour socks, 1 more of any colour to make a pair. In b) you have the 4 socks already, then you can have 3 different colours. however, if you pull out one of the same colour as the original pair, you have 1 pair, and 3 socks. After this, you are back to the beginning. So far you have 5 socks out. The next sock you pull out will make a pair, meaning you have 2 matching pairs. This means you have 6 socks in total.
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  5. #5
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by greatersanta616 View Post
    I dont know how to do quote. hehe.
    To quote you can use the "reply with quote" button, or the multi-quote button, or you can use [quote][/quote] tags

    Quote Originally Posted by greatersanta616 View Post
    in the question above, it does not state whether you need 2 pairs of the same colour, or two different colours, so the right answer is not 10.
    I see where the confusion came from though. "two matching pairs of socks" is not far away from "two matching pairs of matching socks."
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