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schmidtdancer

Back to the cards! In poker, a flush is when all five cards are the same suit. Find the probability of being dealt a flush (when being dealt five cards). Start by just considering clubs.

  • one year ago
  • one year ago

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  1. schmidtdancer
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    a) What is the probability that the first card dealt is a club? b) What is the probability that the second card dealt is a club given that the first one was a club? c) What is the probability that the third card dealt is a club given that the first two were clubs? d) What is the probability that the fourth card dealt is a club given that the first three were clubs? e) What is the probability that the fifth card dealt is a club given that the first four were clubs? f) The probability of being dealt all five clubs is the product of the above probabilities. Why is this true and what is this probability? g) You have now found the probability of being dealt a flush in clubs. This is the same as the probability of being dealt a flush in diamonds, hearts, or spades. Then, what is the proability of being dealt a flush?

    • one year ago
  2. hba
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    How many cards in a deck ?

    • one year ago
  3. schmidtdancer
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    Umm... im not sure

    • one year ago
  4. schmidtdancer
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    @mathmate

    • one year ago
  5. schmidtdancer
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    @Hero @radar

    • one year ago
  6. schmidtdancer
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    @marsss

    • one year ago
  7. EulerGroupie
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    There are 52 cards in a standard deck. Divide by 4 to get the number of cards of each suit.

    • one year ago
  8. radar
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    That would mean there are 13 club cards out of 52 cards. Wouldn't that mean the probability of drawing a club is 1 out of 4?

    • one year ago
  9. mathmate
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    Yes, drawing the first club out of the full deck of 52 cards has a probability of 1 out of 4, or 0.25. What about the probabiliity of the second card: - how many clubs are left (assuming first one is a club) ? - how many cards are left in the deck?

    • one year ago
  10. radar
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    Now on the 2nd draw there would be 13 club cards out of 51 3rd draw 12 out of 50 4th draw 11 out of 49 5th draw 10 out of 48

    • one year ago
  11. mathmate
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    ...huh?

    • one year ago
  12. radar
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    Wouldn't that be the chances for each draw assuming he draws into a 5 card flush. Now take the product of all those chances to get the probability. 1/4 * 13/51 * 6/25 * 11/49 * 5/24

    • one year ago
  13. radar
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    I would guesstimate a little less than 1400 to 1

    • one year ago
  14. radar
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    What does google say?

    • one year ago
  15. schmidtdancer
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    hey I'm here now

    • one year ago
  16. schmidtdancer
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    so a i got 1/4. what is b?

    • one year ago
  17. radar
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    Chance according to Google is 0.003940. or about 254 to 1 so it looks like I probably erred.

    • one year ago
  18. schmidtdancer
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    so b is 254/1?

    • one year ago
  19. schmidtdancer
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    or .004?

    • one year ago
  20. radar
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    I am afraid I have been away from those kind of problems too long. Hopfully, @mathmate will provide further assistance.

    • one year ago
  21. schmidtdancer
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    Do u know anyone online right now that can give me assistance now?

    • one year ago
  22. schmidtdancer
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    @Agent_Sniffles

    • one year ago
  23. schmidtdancer
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    @zepdrix

    • one year ago
  24. radar
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    The Google solution involved a flush in any suit not just clubs.

    • one year ago
  25. schmidtdancer
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    huh?

    • one year ago
  26. radar
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    The probability of a flush can occur in hearts, diamonds, spades or clubs, just as long as all cards are the same suit!

    • one year ago
  27. schmidtdancer
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    So what would my answers be?

    • one year ago
  28. radar
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    You requested the probability of a flush in clubs only.

    • one year ago
  29. schmidtdancer
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    Yea. thats what the question said

    • one year ago
  30. schmidtdancer
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    how would I start answering B?

    • one year ago
  31. radar
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    I answered that, if the first one was a club, you now have a deck of 51 cards of which 12 are clubs; 12/51 or 0.235294

    • one year ago
  32. schmidtdancer
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    Ok so b would then be 12/51?

    • one year ago
  33. radar
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    Here is mathmate. hopefully shed some light on this.

    • one year ago
  34. schmidtdancer
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    I have (a) 1/4 (b) 12/51 now c?

    • one year ago
  35. radar
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    Ask yourself how many cards are now in the deck, how many are clubs and figure out the probability using the method you have been taught.

    • one year ago
  36. mathmate
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    Sorry for being away. @radar sorry, I was just questioning in case there was a typo. For (b) After the first card, there are 13-1=12 clubs left out of 51. So the probability is 12/51. Or, using conditional probabilities: P(1)=13/52 P(1&2)=13/52*12/51 P(2|1)=P(2&1)/P(1)=(13/52*12/51) / (13/52) = 12/51, same as before.

    • one year ago
  37. schmidtdancer
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    Okay I got that for (b) too!:) Im not sure how to find c now

    • one year ago
  38. radar
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    Sorry but I have to now run, you are in good hands.

    • one year ago
  39. schmidtdancer
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    Would (c) be 11/51 then?

    • one year ago
  40. mathmate
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    @schmidtdancer The questions are made in such a way to guide you to the final answer. I suggest that after a and b have been explained and answered, it would be advantageous for you to continue the logic and post your suggested responses for verification. What do you think?

    • one year ago
  41. schmidtdancer
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    ? I just need clarification on how to find C. can u guide me through the steps....and ill figure it out by myself then u can check?

    • one year ago
  42. schmidtdancer
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    @mathmate

    • one year ago
  43. schmidtdancer
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    @precal

    • one year ago
  44. mathmate
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    Sure!

    • one year ago
  45. schmidtdancer
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    Thanks! how do i begin c?

    • one year ago
  46. schmidtdancer
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    c) What is the probability that the third card dealt is a club given that the first two were clubs?

    • one year ago
  47. mathmate
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    For the third club in a row, how many clubs are left? and how many cards are left in the deck?

    • one year ago
  48. schmidtdancer
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    since there are 14 clubs in a set, then we would have 11 left right?

    • one year ago
  49. schmidtdancer
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    because b is 12/51? and were losing another so would c be 11/51?

    • one year ago
  50. mathmate
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    I'll make it clear: After the first two clubs are drawn and before we draw the third card, how many clubs remain in the deck, and how many cards total remain?

    • one year ago
  51. schmidtdancer
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    there are 14 clubs total in a deck... and 52 cards total in a deck... so, after two are drawn, then we have 12 clubs and 50 cards?

    • one year ago
  52. schmidtdancer
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    is that for b or c?

    • one year ago
  53. schmidtdancer
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    @mathmate ????

    • one year ago
  54. schmidtdancer
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    @countonme123

    • one year ago
  55. mathmate
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    Each deck has 52 cards, divided by 4 suits gives 13 cards per suit to start with (not 14). (a) before drawing any card, we have 13 clubs and 52 cards. (b) given the first card drawn was a club, before drawing the second card, we have 12 clubs and 51 cards. (c) given the first 2 cards drawn were clubs, before drawing the third card, we have how many clubs and how many cards in the deck?

    • one year ago
  56. schmidtdancer
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    10/49?

    • one year ago
  57. schmidtdancer
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    @mathmate

    • one year ago
  58. mathmate
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    We have only drawn 2 clubs out of 13, how many left?

    • one year ago
  59. schmidtdancer
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    11

    • one year ago
  60. mathmate
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    Sorry, the OS seems to be very selective in response. I cannot get to your question unless I go by your profile. When I go by "mathematics", it never responds for the past two days.

    • one year ago
  61. schmidtdancer
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    Its ok. but is 11 right?

    • one year ago
  62. mathmate
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    (c) Also, drawn two cards (clubs) out of 52, how many left?

    • one year ago
  63. schmidtdancer
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    50

    • one year ago
  64. schmidtdancer
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    so 11/52 would be c?

    • one year ago
  65. schmidtdancer
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    I mean 11/50!!!!

    • one year ago
  66. schmidtdancer
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    right @mathmate

    • one year ago
  67. mathmate
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    Yes, that is correct for (c). Again, your response was not updated. I had to check through you profile every time I suspect a response. You're comfortable continuing?

    • one year ago
  68. schmidtdancer
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    Okay, and yes

    • one year ago
  69. schmidtdancer
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    How would I find (d) now @mathmate

    • one year ago
  70. mathmate
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    Each deck has 52 cards, divided by 4 suits gives 13 cards per suit to start with (not 14). (a) before drawing any card, we have 13 clubs and 52 cards. (b) given the first card drawn was a club, before drawing the second card, we have 12 clubs and 51 cards. (c) given the first 2 cards drawn were clubs, before drawing the third card, we have how many clubs and how many cards in the deck? (d) given the first 3 cards drawn were clubs, before drawing the fourth card, we have how many clubs and how many cards in the deck?

    • one year ago
  71. schmidtdancer
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    so (d) is: 10/49?

    • one year ago
  72. schmidtdancer
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    This is what I have.... is it correct @mathmate ? (a) 1/4 (b) 12/51 (c) 11/50 (d) 10/49 (e) 9/48

    • one year ago
  73. mathmate
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    Looks good so far. Keep it up, you're almost there!

    • one year ago
  74. schmidtdancer
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    Im a little confused on f and g!

    • one year ago
  75. mathmate
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    Have you done conditional probability before?

    • one year ago
  76. schmidtdancer
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    Kinda

    • one year ago
  77. schmidtdancer
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    When it says product, do I just multiply a-e?

    • one year ago
  78. schmidtdancer
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    ?@mathmate

    • one year ago
  79. mathmate
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    Yes, the numerical part is just the product of the 5 probabilities. Give me a minute for the explanation part of (f). Once you have the numerical probability of clubs obtained in (f), how would you propose to find (g)?

    • one year ago
  80. schmidtdancer
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    so f is then: 11880/23990400??

    • one year ago
  81. schmidtdancer
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    @mathmate

    • one year ago
  82. schmidtdancer
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    Then would g be the decimal value of f?

    • one year ago
  83. mathmate
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    It's almost correct, but you need to simplify it to the simplest form. Can you do that?

    • one year ago
  84. schmidtdancer
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    I was gonna ask u lol, I'm not sure how to simplify it... im trying

    • one year ago
  85. mathmate
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    No. Think of (g) is for the case where there are 4 suits instead of just clubs. Imagine buying raffle tickets. What are the changes of winning if you bought 4 instead of one?

    • one year ago
  86. schmidtdancer
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    I have 495/999600 so far

    • one year ago
  87. schmidtdancer
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    for f..

    • one year ago
  88. schmidtdancer
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    33/66640

    • one year ago
  89. schmidtdancer
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    Is this f?? 33/66640

    • one year ago
  90. mathmate
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    Factors that you can cancel are like 36...

    • one year ago
  91. schmidtdancer
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    is this right @mathmate 33/66640

    • one year ago
  92. mathmate
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    That is correct.

    • one year ago
  93. schmidtdancer
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    Ok thank you! now, g?

    • one year ago
  94. mathmate
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    Now try (g)

    • one year ago
  95. schmidtdancer
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    hmm?

    • one year ago
  96. schmidtdancer
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    g) You have now found the probability of being dealt a flush in clubs. This is the same as the probability of being dealt a flush in diamonds, hearts, or spades. Then, what is the proability of being dealt a flush?

    • one year ago
  97. schmidtdancer
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    im not sure what its asking for an answer....@mathmate

    • one year ago
  98. mathmate
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    Means a flush of any of the 4 suits. Imagine buying raffle tickets. What are the changes of winning if you bought 4 instead of one?

    • one year ago
  99. mathmate
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    *chances

    • one year ago
  100. schmidtdancer
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    4 times as much?@mathmate

    • one year ago
  101. schmidtdancer
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    ?

    • one year ago
  102. mathmate
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    Right! That's. I hope you are better prepared for the next question.

    • one year ago
  103. schmidtdancer
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    But what would g be??

    • one year ago
  104. schmidtdancer
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    Is the answer: 4 times as much? @mathmate

    • one year ago
  105. mathmate
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    4 times what you got for (f).

    • one year ago
  106. schmidtdancer
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    so is it: .002?

    • one year ago
  107. schmidtdancer
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    132/266560 in fraction form <-- is this the answer @mathmate

    • one year ago
  108. mathmate
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    I would rather put it as 4*(33/66640) =33/16660. In probabilities, small numbers like 0.002 is better represented by fractions.

    • one year ago
  109. schmidtdancer
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    thx! so g @mathmate is 33/16660?

    • one year ago
  110. schmidtdancer
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    but thats lower than f.

    • one year ago
  111. mathmate
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    Yes. I am sorry it is probably painful for you as much as for me because the system does not respond (does not update). So I don't really know when you put in a response.

    • one year ago
  112. schmidtdancer
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    its ok but @mathmate how is g 33/16660? when f is higher than that value?

    • one year ago
  113. mathmate
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    When the denominator is 4 times smaller, it means that the fraction is 4 times bigger. For example, 1/4 is smaller than 1/1.

    • one year ago
  114. schmidtdancer
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    Oh oak!! thanks for all your help

    • one year ago
  115. mathmate
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    You're welcome! Good luck with your homework/exam! :)

    • one year ago
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