Find the probability of drawing a flush in 5-card poker.
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.
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.
To find the probability of drawing a flush in 5-card poker, we need to determine the number of possible flush hands and divide it by the total number of possible 5-card hands.
1. Determine the number of possible flush hands:
In a standard deck of 52 cards, there are 13 cards of each suit (spades, hearts, diamonds, and clubs). To form a flush, we need all 5 cards to be of the same suit. Therefore, there are 4 possible suits to choose from.
Choose 1 of these suits: 4 suits
For each suit, we need to choose 5 cards:
Choose 5 cards of the chosen suit: C(13, 5) = (13!)/(5!(13-5)!) = 1,287
2. Determine the total number of possible 5-card hands:
From a 52-card deck, we need to choose 5 cards without considering their order.
Choose 5 cards from a deck of 52: C(52, 5) = (52!)/(5!(52-5)!) = 2,598,960
3. Calculate the probability:
The probability of drawing a flush is equal to the number of possible flush hands divided by the total number of possible 5-card hands.
Probability of drawing a flush = (Number of flush hands) / (Total number of 5-card hands)
Probability of drawing a flush = 1,287 / 2,598,960
Probability of drawing a flush ≈ 0.00196 or 0.196%