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Suppose that you are playing hold ’em, and you are dealt Qhearts 10hearts . Afte

ID: 3044060 • Letter: S

Question

Suppose that you are playing hold ’em, and you are dealt Qhearts 10hearts . After this, five card are eventually laid face-up on the table. The hand you end up with is the best possible hand made up of five of the seven cards available to you: your two plus the five on the table. a) What is the probability that your hand will be a royal flush? b) What is the probability that your hand will be a straight flush? c) What is the probability that your hand will be a straight? d) What is the probability that your hand will be a flush? Suppose that you are playing hold ’em, and you are dealt Qhearts 10hearts . After this, five card are eventually laid face-up on the table. The hand you end up with is the best possible hand made up of five of the seven cards available to you: your two plus the five on the table. a) What is the probability that your hand will be a royal flush? b) What is the probability that your hand will be a straight flush? c) What is the probability that your hand will be a straight? d) What is the probability that your hand will be a flush? Suppose that you are playing hold ’em, and you are dealt Qhearts 10hearts . After this, five card are eventually laid face-up on the table. The hand you end up with is the best possible hand made up of five of the seven cards available to you: your two plus the five on the table. a) What is the probability that your hand will be a royal flush? b) What is the probability that your hand will be a straight flush? c) What is the probability that your hand will be a straight? d) What is the probability that your hand will be a flush?

Explanation / Answer

Solution:-

a) The probability that the hand is a royal flush is 0.00000154.

Total combination of royal flush = 4

Total number of combinations of different hands = 52C5 = 2,598,960

The probability that the hand is a royal flush is = 4/2598960 = 0.00000154.

b) The probability that the straight flush including royal flush is 0.0000154.

Each straight flush is uniquely determined by its highest-ranking card. These ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits.

The number of such hands = 36 + 4 = 40

Total number of combinations of different hands = 52C5 = 2,598,960

Probability of straight flush including royal flush is = 40/2598960 = 0.0000154

c) Probability of straight is 0.003925.

Here all 5 cards are from the same suit

The number of such hands = (10C1 × (4C1)5 ) - 40= 10,200

Total number of combinations of different hands = 52C5 = 2,598,960

Probability of straight = 10200/2598960 = 0.003925

d) Probability of flush = 0.00198079.

Here all 5 cards are from the same suit

The number of such hands =4C1 × 13C5 = 5148

Total number of combinations of different hands = 52C5 = 2,598,960

Probability of flush = 5148/2,598,960 = 0.00198079.

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