Answer
Success!
Decimal probability = 1.38517E-5
↓Steps Explained:↓
In a standard 5-card poker hand for 1 deck:
Calculate P(Straight Flush)
Straight 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 Straight Flushes = Possible ways to get 5 cards in a row starting with A-9 card
Possible Straight Flushes = 9 ways * 4 possible suits (Spade,Heart,Diamond,Club) = 36
| P(Straight Flush) = | Straight Flushes |
| Total Hands |
Reduce top and bottom by 12
GCF = Greatest Common Factor
| P(Straight Flush) = | 36 |
| 2,598,960 |
GCF for 3 and 216580 = 12
| P(Straight Flush) = | 3 |
| 216,580 |
Final Answer
Decimal probability = 1.38517E-5Take the Quiz
Related Calculators: Hypergeometric Distribution | Hardy-Weinberg | Fishers Exact Test