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Math Help - Probability

  1. #1
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    Probability

    For a game of poker, a person is dealt 5 cards from a standard deck. Find the probability of getting:

    a) 4 aces
    b) a flush (all cards the same suit)

    I've tried ways of doing it. I've gotten the answer before, but I don't understand what I'm doing. Any help is appreciated.
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  2. #2
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    Quote Originally Posted by Gusbob View Post
    For a game of poker, a person is dealt 5 cards from a standard deck. Find the probability of getting:

    a) 4 aces
    b) a flush (all cards the same suit)

    I've tried ways of doing it. I've gotten the answer before, but I don't understand what I'm doing. Any help is appreciated.
    a) \frac{{4 \choose 4} {48 \choose 1} }{{52 \choose 5}} = ......

    b) 4 \, \frac{{13 \choose 5} {39 \choose 0} }{{52 \choose 5}} = ......
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  3. #3
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    a) 4/52 + 3/51 + 2/50 + 1/49 + 48/48

    b)13/52 + 12/51 + 11/50 + 10/49 + 9/48

    Sorry i dont know how to use the proper diagrams like everyone else

    Thats assuming your dealing only to yourself
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  4. #4
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    I took these off a few gambling sites like this one:

    Flush:
    Probability and the Flush in Poker - InDepthInfo

    You can see a writeup of the different combinations here too.

    5 Card Poker Probabilities

    I confirmed those probabilities off a few poker sites. I programmed the math to walk through the different scenarios. That's for 1 standard deck of 52 cards, no jokers, dealt only to you. That doesn't show 4 aces however.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    a) \frac{{4 \choose 4} {48 \choose 1} }{{52 \choose 5}} = ......

    b) 4 \, \frac{{13 \choose 5} {39 \choose 0} }{{52 \choose 5}} = ......
    Thank you. I understand almost all of it, but what does the  {39 \choose 0} mean in part b?
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  6. #6
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    Quote Originally Posted by Gusbob View Post
    Thank you. I understand almost all of it, but what does the  {39 \choose 0} mean in part b?
    Gusbob, 2 things.

    1) Fantastic is off line right now. What he means by that expression is a combination of 39 items choose 0. Go here Permutation and Combination Calculator

    Enter 39 and 0, and press combinations. That's what the value of his expression is and how to get there. That means out of a group of 39 items, how many unique arrangements can you have.

    2) Also, the link I posted in the prior post subtracts out all straight and royal flushes. After speaking with you, it appears you wanted all kinds of flushes which is what Fantastic did.
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  7. #7
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    What I meant was why the 39 choose 0 was there. But now I see that we are choosing 0 cards from the remaining 39 cards. I always forget the remaining cards
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