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Math Help - 3 cards of the same suit

  1. #1
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    3 cards of the same suit

    From a standard deck, what is the probability of drawing 3 cards of the same suit, without replacement?

    When I do this, I want to go with 4 * (13/52 * 12/51 * 11/50) = 22/425
    However, I am not sure when I look at other sites... probability of drawing 3 cards - Wolfram|Alpha is an example. The specific way I am trying to do this is through compound events, instead of combination or permutation. Any input would be helpful, thank you!
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  2. #2
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    Quote Originally Posted by tcRom View Post
    From a standard deck, what is the probability of drawing 3 cards of the same suit, without replacement?

    When I do this, I want to go with 4 * (13/52 * 12/51 * 11/50) = 22/425
    However, I am not sure when I look at other sites... probability of drawing 3 cards - Wolfram|Alpha is an example. The specific way I am trying to do this is through compound events, instead of combination or permutation. Any input would be helpful, thank you!
    Your analysis is correct.

    It's not entirely clear how Wolfram Alpha gets its result, but the answer it gives (approximately 1 in 19) is consistent with yours.
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  3. #3
    MHF Contributor matheagle's Avatar
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    I would use the hypergeometric.......

    4{{13\choose 3}{39\choose 0}\over {52\choose 3}}={(4)(13)(12(11)\over (52)(51)(50)}\approx .051764706

    BUT from this you can see the conditional probability way to obtain this value...

    4\left({13\over 52}\right)\left({12\over 51}\right)\left({11\over 50}\right)
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  4. #4
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    (12/51) * (11/50) is all you need;
    1st card considered already drawn.
    Question can be:
    a heart is drawn: what is probability that next 2 will be hearts?
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