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Math Help - Can you check please

  1. #1
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    Can you check please

    There are 10 different hats, what is the probability that if I got 4 of them that I would get at least 2 the same?

    Would it be 1/10 * 1/9 * 1/8 * 1/7?

    Thanks in advance.
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  2. #2
    Super Member Deadstar's Avatar
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    Unless I'm missing something then I think more information is needed..?
    How many types of hat are there? Post the ENTIRE question.
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  3. #3
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    10 types of hat which are equally likely to be got.
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  4. #4
    Super Member Deadstar's Avatar
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    Ok but how many hats are there in total? If there's only ten then you can't get two the same.
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  5. #5
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    Ok I see now, 10 different types of hat but presumably infinite hats in total. The question is ' if you get four attempts you will obtain at least 2 of the same type'.
    You only have 4 attempts to choose.
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  6. #6
    Super Member Deadstar's Avatar
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    Maybe this is wrong but I think it's...

    1-Probability(all hats are different)

    So you get your first hat with prob 1.
    The prob that the second one is different is 9/10
    The prob that the third one is different is 8/10
    The prob that the fourth one is different is 7/10

    So 1-Probability(all hats are different) = 1-(9/10*8/10*7/10) = 0.496.
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  7. #7
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    Quote Originally Posted by bigroo View Post
    Ok I see now, 10 different types of hat but presumably infinite hats in total. The question is ' if you get four attempts you will obtain at least 2 of the same type'.
    You only have 4 attempts to choose.
    There are \binom{4+10-1}{4} total number of ways to choose four hats.
    There are \binom{10}{4} ways to choose four hats all of different types.
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  8. #8
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    Quote Originally Posted by Deadstar View Post
    Maybe this is wrong but I think it's...

    1-Probability(all hats are different)

    So you get your first hat with prob 1.
    The prob that the second one is different is 9/10
    The prob that the third one is different is 8/10
    The prob that the fourth one is different is 7/10

    So 1-Probability(all hats are different) = 1-(9/10*8/10*7/10) = 0.496.
    So my answer was nearly the same as yours but instead of 1/10 you have 1.
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  9. #9
    Super Member Deadstar's Avatar
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    Quote Originally Posted by bigroo View Post
    So my answer was nearly the same as yours but instead of 1/10 you have 1.
    Plato will be right.
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