# Prob and stat poker probability question

1. Jan 8, 2009

### Proggy99

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 $$\left(\stackrel{52}{5}\right)$$ different poker hands

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

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. Jan 8, 2009

Looks right.

3. Jan 8, 2009

### Proggy99

thanks for taking a look