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    ATenjum's Avatar
    ATenjum Posts: 1, Reputation: 1
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    #1

    Jan 4, 2011, 05:08 PM
    Playing Cards
    You have a standard 52 card playing card deck. You then add 2 Jokers for a total of 54 cards and shuffle the deck. If you draw cards one by one, what is the probability that you draw the Queen of Hearts before you draw a Joker?
    ma0641's Avatar
    ma0641 Posts: 15,675, Reputation: 1012
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    #2

    Jan 4, 2011, 06:43 PM
    Pretty basic math. 1 queen of hearts in 54 cards=1/54. 2 jokers in 54 cards 2/54=1/27 2:1 jokers, 1/2:1 queen.
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #3

    Jan 5, 2011, 06:04 AM

    Are you replacing or not?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Jan 5, 2011, 10:02 AM
    Quote Originally Posted by Capuchin View Post
    are you replacing or not?
    I don't think it matters.

    If not replacing, then all you need worry about are three cards - call them A, B and C. This question is equivalent to asking if you shuffle the deck what is the probability that card A comes before both B and C in the deck. That's 1/3.

    If you are replacing, then the probability of getting card A on any one draw is 1/2 the probability of drawing either B or C. So the probability of getting A before B or C is (1/2)/(1+1/2) = 1/3.
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #5

    Jan 5, 2011, 10:28 AM

    It's true that it doesn't matter, I was asking to try and help some thought processes along :)
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