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Math Help - Probability, distribution and covariance with a deck of 52 cards

  1. #1
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    Probability, distribution and covariance with a deck of 52 cards

    Here is my problem,

    Start with a standard, uniformly shued 52-card deck, and draw the cards one at a
    time.

    (a) What is the probability of drawing a King strictly before getting a Spade?
    (b) What is the distribution of the number of Jacks drawn after the last Queen is drawn?
    (c) Let X1 be the position at which the 1rst Spade is drawn, and X2 the position at which the 1 rst Club is drawn. Calculate the distribution of X1.

    For (a), I tried by conditionning probability, combinatory and a long sum of probability which gave me 3/16 but my solution is really too long so I don't think I'm using the shortest method here. Do you have any shortcut?

    For (b) I don't understand quietly how to find the distribution?

    For (c) of course there is a covariance because drawing one or the other will have an influence on the position of the next card, but how to calculate such a covariance.

    Thank you
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  2. #2
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591

    Re: Probability, distribution and covariance with a deck of 52 cards

    Quote Originally Posted by solvj View Post
    Here is my problem,

    Start with a standard, uniformly shued 52-card deck, and draw the cards one at a
    time.

    (a) What is the probability of drawing a King strictly before getting a Spade?
    (b) What is the distribution of the number of Jacks drawn after the last Queen is drawn?
    (c) Let X1 be the position at which the 1rst Spade is drawn, and X2 the position at which the 1rst Club is drawn. Calculate the distribution of X1.

    For (a), I tried by conditionning probability, combinatory and a long sum of probability which gave me 3/16 but my solution is really too long so I don't think I'm using the shortest method here. Do you have any shortcut?

    For (b) I don't understand quietly how to find the distribution?

    For (c) of course there is a covariance because drawing one or the other will have an influence on the position of the next card, but how to calculate such a covariance.

    Thank you
    a) There are 13 spades and 4 kings, one of the kings is the king of spades. There are 16 cards to worry about. Of these 16 cards you win if one of the 3 non-spade kings is first. Does that help ?

    b) Here there are 8 cards to worry about and you are looking at how the sequence ends. You want to know the probability of it ending:

    Q - no jacks drawn after the last queen
    QJ - one drawn
    QJJ - two
    QJJJ- three
    JJJJ - four

    c) why are you calculating the covariance ? I don't understand how you are approaching this problem.
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