Answer
Success!
Decimal probability = 0.0019654015
↓Steps Explained:↓
In a standard 5-card poker hand for 1 deck:
Calculate P(Flush)
Flush Hands
Calculate Total 5 Card hands
| Total Hands = | 52! |
| (52-5)! * 5! |
| Total Hands = | 52! |
| 47! * 5! |
| Total Hands = | (52 * 51 * 50 * 49 * 48) * 47! |
| 47! * (5 * 4 * 3 * 2 * 1) |
Cancelling the 47!, we get:
| Total Hands = | 311,875,200 |
| 120 |
Total Hands = 2,598,960
Build Probability
Possible flushes = Possible ways to get 5 of the same suit.
Possible flushes in one suit * 4 suits = 13! * 4/((13 - 5)! * 5!) = 5,108 ways
Total Possible flushes * 4 possible suits = (13 * 12 * 11 * 10 * 9 * 4) / (5 * 4 * 3 * 2 * 1)
Possible flushes - (36 straight . 4 Royal {Flushes}) = (617,760 / 120) - 40
Possible flushes = 5,148 - 40
Possible flushes = 5108
| Probability of a flush = | Possible flushes |
| Total Hands |
Reduce top and bottom by 4
GCF = Greatest Common Factor
| P(Flush) = | 5,108 |
| 2,598,960 |
| P(Flush) = | 1,277 |
| 649,740 |
Final Answer
Decimal probability = 0.0019654015Take the Quiz
Related Calculators: Hypergeometric Distribution | Hardy-Weinberg | Fishers Exact Test