We assume that the game of poker is played using a randomized standard deck of 52 cards. Each hand is randomly dealt 5 cards.
Find the probability of being dealt each of the poker hands below.
1. A pair. Exactly two of the same denomination.
2. Three-of-a-kind. Exactly three of the same denomination.
3. Four-of-a-kind. Exactly four of the same denomination.
4. Two pair. Two pairs of distinct denominations and a fifth card which doesn’t match either pair.
5. Full house. Three-of-a-kind and a pair.
6. Flush. All five cards have the same suite.
7. Straight. Five consecutive denominations, where Ace can either be treated as the low or high card.
8. Straight flush. A straight where all cards have the same suite.
9. Royal flush. A straight flush that begins with 10.