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Prob and stat poker probability question

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data
    On average, how many times should Ernie play poker in order to be dealth a straight flush (royal flush included)?

    2. Relevant equations
    There are 10 ways to get a straight flush for each suit (ace thru 10 as the starting card), so there are 40 total ways for a straight flush.
    There are [tex]\left(\stackrel{52}{5}\right)[/tex] different poker hands

    So where A is a straight flush, [tex]p(A) =\frac{40}{\left(\stackrel{52}{5}\right)}=.0000154[/tex]

    3. The attempt at a solution
    To find the number of times he must play in order to get one straight flush, I am using the equation np = x where x = 1
    np = 1
    n(.0000154) = 1
    n = 1/.0000154 = 64,935.065 times

    I am pretty confident in my answer but I do not have the answer to verify this. Can anyone confirm this for me or give me a hint as to where I might be going wrong? Thanks!
  2. jcsd
  3. Jan 8, 2009 #2
    Looks right.
  4. Jan 8, 2009 #3
    thanks for taking a look
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