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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