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Math Help - Playing cards

  1. #1
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    Playing cards

    Please help!

    We are playing a card game, where we have a big discusion about statistic. Hope one of you can help solving the problem.

    I have the card spades 2. 3 other persons each recieve a single card - 3 in total.

    How big is chance that one of the 3 persons recieve a spades? All 52 cards are used - after I have received spades 2 there are 12 spades back of a total of 51 card.

    Please help, or write back, if you need further information to answer the question.

    Kind Regard
    Kim
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  2. #2
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    Re: Playing cards

    Each of them has a probability of 12/51 of having another spade.
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  3. #3
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    Re: Playing cards

    I agree, but how big is the chance in total, that one of the three have a spade? I think it is 36/51. Right?
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    Re: Playing cards

    It is a bit hard to follow your setup. Say you have one card, a spade, then you deal one card to each of two other people. I think that you want to know the probability their getting at least one spade.
    The probability their getting no spade is \frac{39\cdot 38}{51\cdot 50}.

    So the probability their getting at least one spade is 1-\frac{39\cdot 38}{51\cdot 50}.
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    Re: Playing cards

    Hi Plato

    I play a card game with 4 players involved. I have a spade, and want to know how big (percent) a chance there is, that one of the 3 other players getting a spade.
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  6. #6
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    Re: Playing cards

    Quote Originally Posted by KimN View Post
    I play a card game with 4 players involved. I have a spade, and want to know how big (percent) a chance there is, that one of the 3 other players getting a spade.
    How many cards are dealt? Are you thinking one card each?
    So four cards in all. If so it is done exactly as I did with three people.
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    Re: Playing cards

    I have one card - eg. spade 2. Then there is 51 cards back. Of these 51 cards i give one card to 3 persons. Then 48 cards back. How many percent chance is it that one of the 3 persons have a spade?
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    Re: Playing cards

    Quote Originally Posted by KimN View Post
    I have one card - eg. spade 2. Then there is 51 cards back. Of these 51 cards i give one card to 3 persons. Then 48 cards back. How many percent chance is it that one of the 3 persons have a spade?
    1-\frac{39\cdot 38\cdot 37}{51\cdot 50\cdot 49}
    That is the probability that at least one of the other three players gets a spade.
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  9. #9
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    Re: Playing cards

    Quote Originally Posted by Plato View Post
    1-\frac{39\cdot 38\cdot 37}{51\cdot 50\cdot 49}
    I agree with Plato.
    That comes out to .56115..., or approximately 11/20

    Your question could be stated this way:
    a spade is missing from a regular 52cards deck;
    3 cards are pulled at random from the remaining 51 cards:
    what is probability that at least one card pulled is a spade?
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