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

    Dec 7, 2008, 03:09 PM
    What is probability of drawing at least one spade
    Three cards are drawn from a standard deck without replacement.
    What is the probability of drawing at least one spade.
    What is the probability of drawing a Jack, Queen, and King in any order.
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 8, 2008, 11:14 AM

    Here are a few hints for you:

    For the first question, you can solve this by doing either of the following:

    1A. The probability of pulling at least one spade is the same as the probability of pulling exactly 1 spade PLUS the probability of pulling exacty 2 spades PLUS the probability of pulling exactly 3 spades.
    1B. The probability of pulling at last one spade is 1 minus the probability of pulling exactly 0 spades.

    Method B is usually easier to calculate, so try that. However, for homework practice I would recommend trying it both ways to verify that you can do it.

    For the second problem - again there are two ways to do it:

    2A. First calculate the probability of pulling the three cards in a presecribed order - such as first a jack followed by a queen followed by a king - and then multiplying this by the number of possible different ways that a jack, queen and king can be arranged. That gets you to where the jack, queen and king can be pulled in any order.
    2B. Realize that on the first draw you have 12 possible "winners" (any of the four jacks, queens or kings in the deck) out of the 52 cards in the deck. On the second draw there are 8 possible winners left in 51 remaining cards of the deck, and for the third draw there are only 4 winners left out of 50 cards.

    As above, I recommend you try solving this problem both ways and confirm that you get the same answer.

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