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mathishard2

  • one year ago

A man has five pairs of socks (no two pairs are the same color). If he randomly selects two socks from a drawer, what is the probability that he gets a matching pair?

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  1. izzy56658989
    • one year ago
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    1/2 chances or 5/10

  2. mathishard2
    • one year ago
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    The answer in the book says 1/9...

  3. izzy56658989
    • one year ago
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    i never said it was gonna be right there was a half chance i was wrong

  4. mathishard2
    • one year ago
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    I'm not trying to show that you're wrong... I just wanted to see if someone could explain this question to me. Because math is hard. And I have a test on probablility tomorrow.

  5. izzy56658989
    • one year ago
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    k there's 5 there it's an uneven number which means if u tryed to pair them all up 1 would be left behind

  6. izzy56658989
    • one year ago
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    lik if u got rid of that 1 sock and did 4x2 =8+1=9

  7. izzy56658989
    • one year ago
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    there's ur denominator

  8. satellite73
    • one year ago
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    he picks one sock it is some color

  9. satellite73
    • one year ago
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    then there are 9 socks left in the drawer, and only one has the same color as the sock he picked originally

  10. izzy56658989
    • one year ago
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    exactly it never said they were the same colors

  11. satellite73
    • one year ago
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    so the probability that the next sock he picks has the same color is \(\frac{1}{9}\)

  12. satellite73
    • one year ago
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    it is easier to think about it if you imagine picking one at a time instead of two at once

  13. satellite73
    • one year ago
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    we can also solve with thinking of picking two at once the number of ways he can pick the two socks out of the total of ten socks is \[\dbinom{10}{2}=\frac{10\times 9}{2}=5\times 9=45\] of those 45 ways, 5 of them are pairs that match, so you get the probability as \[\frac{5}{45}=\frac{1}{9}\]

  14. satellite73
    • one year ago
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    i think the first way is easier to envision, but it is a matter of taste i suppose

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