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Algebra -> Probability-and-statistics-> SOLUTION: A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poke Log On
Common Poker Out Scenarios. Some common poker hand odds are open-ended straight draws at 4.8:1, four to a flush at 4.1:1, inside straight (belly buster) at 10.5:1, one pair drawing to two.
- Running it twice (sometimes called doing business) is a method of determining the winner of a poker hand once all betting on the hand is complete but before the final card(s) (either community cards or other cards) have been dealt. In practice, this is only done when the hand has gotten down to heads up and one player is all-in and the other player has matched their bet. Running it twice can.
- There's no better training for the beginner or average poker player then to see what other poker players would do in certain hand scenarios. Rule 1 of Poker: Keep Learning From Your Mistakes; Rule 2: Never Talk About Rule 1! Poker Hand Evaluations.
Poker Hand Scenarios
Question 1119661: A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places.
a) Determine the probability that exactly 3 of these cards are Aces.
b) Determine the probability of selecting exactly 2 Aces and exactly 2 Kings
c) Determine the probability of selecting exactly 1 Jack.
Answer by greenestamps(7945) (Show Source): You can put this solution on YOUR website!
These are all straightforward probability questions that can be answered using the 'n choose r' concept and basic rules of probability.
The number of possible hands is '52 choose 5':
C(52,5) = 2598960.
(a) To get exactly 3 aces, you need to choose 3 of the 4 aces and 2 of the other 48 cards. The number of ways to do that is
C(4,3)*C(48,2) = 6768
The probability of getting exactly 3 aces is then 6768/2598960 = .0026
(b) To get exactly 2 aces and 2 kings, you need to choose 2 of the 4 aces, 2 of the 4 kings, and 1 of the other 44 cards. The number of ways to do that is
C(4,2)*C(4,2)*C(44,1) = 1584
The probability is then 1584/2598960 = .00006 (.0001, to 4 decimal places)
(c) To get exactly 1 jack, you need to choose 1 of the 4 jacks and 4 of the other 48 cards. The number of ways to do that is
C(4,1)*C(48,4) = 778320
The probability is then 778320/2598960 = .2995
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