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Pulsified333

  • one year ago

A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit).

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  1. dan815
    • one year ago
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    |dw:1442546703792:dw|

  2. Pulsified333
    • one year ago
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    you are very artistic my friend

  3. dan815
    • one year ago
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    chance of 5 cards being all diamond + 5 cards being all heart, all clubs , all spades

  4. dan815
    • one year ago
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    |dw:1442546916458:dw|

  5. dan815
    • one year ago
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    |dw:1442546963874:dw|

  6. anonymous
    • one year ago
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    4 ways to choose a suit * 13 * 12 * 11 * 10 * 9 then divide by 5! because order does not count

  7. dan815
    • one year ago
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    |dw:1442547007019:dw|

  8. anonymous
    • one year ago
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    ( 4 * 13 * 12 * 11 * 10* 9 / 5! ) / (52 choose 5 )

  9. dan815
    • one year ago
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    the same probability with the other suits so 4*(13*12*11*10*9/(52*51*50*49*48))

  10. Pulsified333
    • one year ago
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    so would it be 4(99/199920)

  11. anonymous
    • one year ago
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    ( 4 choose 1 * 13 choose 5 ) /( 52 choose 5 ) =

  12. anonymous
    • one year ago
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    .00198

  13. Pulsified333
    • one year ago
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    i need a fraction

  14. anonymous
    • one year ago
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    5148/2598960

  15. anonymous
    • one year ago
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    = 33/ 16660 , oh cool 666

  16. Pulsified333
    • one year ago
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    it says that 5148/2598960 is wrong

  17. dan815
    • one year ago
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    you must also subtract the case where the cards are consecutive from this as that would be a straight flush or a royal flush

  18. Pulsified333
    • one year ago
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    so how is this done?

  19. dan815
    • one year ago
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    combinatorics is just logic really

  20. dan815
    • one year ago
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    you have to be able to reason through this stuff

  21. dan815
    • one year ago
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    lets take one consecutive flush, like A,2,3,4,5 what is the chance this is drawn

  22. anonymous
    • one year ago
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    33/16660 is wrong?

  23. dan815
    • one year ago
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    need to subtract the consecutuve 5 card case from it jay

  24. dan815
    • one year ago
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    okay so this is how i think you should build up the consecutive case there are 13 pairs of 5 consecutive cards for example A,2,3,4,5 2,3,4,5,6 3,4,5,6,7 . . . Q,K,A,2,3 K,A,2,3,4 what is the chance of each of these cases

  25. anonymous
    • one year ago
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    non straight flushes

  26. anonymous
    • one year ago
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    ( (4 choose 1)*(13 choose 5)-4*10 ) / ( 52 choose 5 )

  27. dan815
    • one year ago
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    close

  28. anonymous
    • one year ago
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    there are 10 straights A,2,3,4,5 2,3,4,5,6 3,4,5,6,7 4,5,6,7,8 5,6,7,8,9 6,7,8,9,10 7,8,9,10, J 8,9,10, J, Q 9,10, J, Q, K 10, J, Q, K, A

  29. dan815
    • one year ago
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    well im not sure they consider KA234 consecutive too actually

  30. anonymous
    • one year ago
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    1277/649740

  31. anonymous
    • one year ago
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    KA234 is a wheel, thats not allowed in texas hold em poker, and most poker variants

  32. dan815
    • one year ago
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    if I was you id try these 3 solutions for your answer ( (4 choose 1)*(13 choose 5)-4*9 ) / ( 52 choose 5 ) ( (4 choose 1)*(13 choose 5)-4*10 ) / ( 52 choose 5 ) ( (4 choose 1)*(13 choose 5)-4*13 ) / ( 52 choose 5 )

  33. Pulsified333
    • one year ago
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    well I have three attempts remaining

  34. dan815
    • one year ago
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    lol

  35. dan815
    • one year ago
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    dont make any calculation mistake xD one of those is definately right haha

  36. Pulsified333
    • one year ago
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    is the 4*10, mean multiply or 4^10?

  37. dan815
    • one year ago
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    40

  38. Pulsified333
    • one year ago
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    okay thank you

  39. dan815
    • one year ago
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    I think you should understand the solution before just answering

  40. Pulsified333
    • one year ago
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    I do now

  41. Pulsified333
    • one year ago
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    would the first one's calculation come out to be 5112/2598960

  42. anonymous
    • one year ago
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    you can use wolfram as a calculator http://www.wolframalpha.com/input/?i=%28+%284+choose+1%29*%2813+choose+5%29-4*10+%29+%2F+%28+52+choose+5+%29

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