In poker, what is the probability of being dealt a straight?
Attempt:
First, we find the size of sample space, the set of all possible 5-hand combinations, this is ${52 \choose 5}$. Now, in how many ways can we obtain a straight? So, this is my thinking,
1) For the first card, we have $14$ possibilities. Let's say we pick an ace. So the other cards must be 2,3,4, and 5.
Notice the ace can be chosen in 4 ways. Now, same argument works until first card is J since then we cant have straight. So we only have $11$ choices. Thus, we have that the number of ways to get straight is
$$ 11 \times 4 \times 14 $$
and hence,
$$ Probability \; \; = \frac{ 11 \times 4 \times 14 }{ {52 \choose 5 } } $$
Is this correct argument?
Best Answer
Your argument is not correct.
A straight is a poker hand consisting of five cards of sequential rank, not all of the same suit.