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Math Help - [SOLVED] probability question

  1. #1
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    [SOLVED] probability question

    A single card id drawn from each of six well shuffled decks of playing card. Let A be the event that all six cards drawn are different.
    (a) find P(A)
    (b) Find the probability that at least two of the drawn card match.

    Please help.

    Thanks
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  2. #2
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    Do we consider 3\heartsuit,\:3\clubsuit as different cards??
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  3. #3
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    Hello, jojo_jojo!

    A single card is drawn from each of six well-shuffled decks of playing cards.
    Let A be the event that all six cards drawn are different.

    (a) Find P(A)

    The first card can be any card: . \frac{52}{52} \,=\,1

    The second can be any of the other 51 cards: . \frac{51}{52}

    The third can be any of the other 50 crds: . \frac{50}{52}

    The fourth can be any of the other 49 cards: . \frac{49}{52}

    The fifth can be any of the other 48 cards: . \frac{48}{52}

    The sixth can be any of the other 47 cards: . \frac{47}{52}


    Therefore: . P(\text{6 different}) \:=\:1\cdot\frac{51}{52}\cdot\frac{50}{52}\cdot\fr  ac{49}{52}\cdot\frac{48}{52}\cdot\frac{47}{52} \;\approx\;0.74




    (b) Find the probability that at least two of the drawn card match.

    The opposite of "no matches" is "at least one match".

    P(\text{at least one match}) \;=\;1-0.74 \;=\;0.26

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  4. #4
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    Thanks a lot!!

    Thanks Soroban .
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