# Any poker players?

• Apr 29th 2012, 02:05 PM
alexgintom
Any poker players?
You are dealt a flush in the game of poker when you are dealt five cards of the same suit. If you are dealt a five-card hand, find the probability you will be dealt a heart flush.
• Apr 29th 2012, 02:43 PM
Plato
Re: Any poker players?
Quote:

Originally Posted by alexgintom
You are dealt a flush in the game of poker when you are dealt five cards of the same suit. If you are dealt a five-card hand, find the probability you will be delt a heart flush.

There are $\displaystyle \dbinom{13}{5}$ ways to select five hearts.
• Apr 29th 2012, 02:56 PM
MathoMan
Re: Any poker players?
Just continuing from the post above.... Classical probability - number of relevant events divided by total number of events: $\displaystyle \frac{ {13 \choose 5}}{{52 \choose 5}}$. One event is choosing 5 cards from a 52 cards deck. Relevant events are those where you ensure that all 5 cards will be of heart suit. So you isolate heart suited cards. From 13 of them you choose 5. There are $\displaystyle {13 \choose 5}$ ways to do that. Now total number of events is the number of ways to choose 5 from 52: $\displaystyle {52 \choose 5}$. Divide those two and you have your probability.
• Apr 29th 2012, 03:13 PM
alexgintom
Re: Any poker players?
How do you divide that with a scientific calculator. I am still learning all the diferent things you can solve with it.
• Apr 29th 2012, 10:06 PM
MathoMan
Re: Any poker players?
Quote:

Originally Posted by alexgintom
How do you divide that with a scientific calculator. I am still learning all the diferent things you can solve with it.

For $\displaystyle {n \choose r}$ use nCr - n Choose r. Input on your calculator should go something like this:
13nCr5÷52nCr5