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Thread: What is the probability of not drawing a club from a deck of cards

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    What is the probability of not drawing a club from a deck of cards




    Hi,
    Can someone help me with this please?

    You draw 40 playing cards, 1 at a time, with replacement from a standard deck.
    What is the probability of NOT drawing a club in 12 successive picks!

    In advance
    Thankyou!

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    Re: What is the probability of not drawing a club from a deck of cards

    I don’t fully understand the question: “draw 40 playing cards” seems to contradict “12 successive picks.”

    Since it’s with replacement, the deck remains intact for each draw. In a standard deck of 52 cards with Jokers excluded, there are 13 Clubs and 39 non-Clubs. Thus, the probability of not drawing a Club (i.e., drawing a non-Club) on any single draw is 39/52 = ¾.

    For n successive draws, the probability of not drawing a Club is compounded because each draw is independent: P_n = \left( \frac{3}{4} \right)^n.

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    Re: What is the probability of not drawing a club from a deck of cards


    Quote Originally Posted by Con-Tester View Post
    I don’t fully understand the question: “draw 40 playing cards” seems to contradict “12 successive picks.”

    Since it’s with replacement, the deck remains intact for each draw. In a standard deck of 52 cards with Jokers excluded, there are 13 Clubs and 39 non-Clubs. Thus, the probability of not drawing a Club (i.e., drawing a non-Club) on any single draw is 39/52 = ¾.

    For n successive draws, the probability of not drawing a Club is compounded because each draw is independent: P_n = \left( \frac{3}{4} \right)^n.
    Hi,
    Sorry for not being clear enough!

    In total you draw 40 cards 1 at a time and replace it before drawing the next card.
    What I want to know is the probability of not drawing 12 clubs on the trot, at any time during the 40 picks

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