Find the probability of drawing a flush in 5-card poker.

Answer 1

There is a probability of 1 for getting the first card. Assuming that you are the only one being dealt, once the first card is obtained, the probability of getting the second card for the flush is 12/51. For the third card. it is 11/50. From this, you should be able to figure the probabilities for the fourth and fifth cards.

The probability of getting all of them is found by multiplying the probability of the individual events.

I hope this helps. Thanks for asking.

Answer 2

or....

no of ways to pick 5 cards of the same suit = 4C(13,5)

number of ways to draw any 5 cards = C(52,5)

so prob of a flush = 4C(13,5)/C(52,5) which gives you the same answer as PsyDAG provided.