same time, and are called \"the flop The fourth card is called \"the turn,\" and
ID: 3170550 • Letter: S
Question
same time, and are called "the flop The fourth card is called "the turn," and the fifth and last card is called "the river." a. Count the total number of distinct combinations of cards" which you could be dealt. This number is important for calculating the next several probabilities. b. What the probability that you are dealt a pair," meaning that your two hole have the same rank? c. What is the probability of one of your hole cards Ace but not both? being an d. the probability of being dealt a "suited connector," meaning that your hole cards have the same suit and adjacent rank one card's rank is exactly one more than the other)? e. at is the probability of being dealt on Ace, a pocket pair, or a suited connector? next four questionsExplanation / Answer
Answer:
1. Total number of distinct combination of hole cards
There are total 52cards in a poker and number different combinations of hole cards can be computed using formula for combinations nCr = 52C2 = 1326. Alternatively, the first card can be any of the 52 cards, the second card could be any of the remaining 51 cards. Total combination = (52*51)/2 = 1326
2. Probability of a pocket pair (two hole cards have the same rank)
There are 13 different unique ranks in poker card. One can get same rank in both cards in different ways like getting AA, 11, 22.. etc. There are 13 such possible pairs. However, these cards can also have different suits amongst 4 possible suits. Therefore total number of possible pocket pairs = 13*4C2 = 13*6 = 78. Probability of getting a pocket pair from a total 1326 possible combinations = 78/1326 = 0.0588
3. Probability of one of the hole card being an Ace but not both: Probability (first hole card is an Ace but second one is not) + probability (first hole card is not an Ace but second hole card is an Ace)
There are 4 Ace’s (4 different suits) in a poker game.
Probability of getting an Ace in first card = 4/52. Probability of getting a card other than Ace from remaining 51 cards = 48/51
Probability of not getting an Ace in first card = 48/52 and Probability of getting an Ace in second card from remaining 51 cards = 4/51
Probability of one hole card being an Ace but not both = (4/52)*(48/51) + (48/52)*(4/51) = 0.144796
4. Suited Connector – hole cards have same suit and adjacent rank
There are 64 possible ways of getting adjacent cards of same rank e.g adjacent hole card 1,2 can appear 4 times (corresponding to 4 different suits). Overall 4*13 = 25 possible ways of getting adjacent rank of same suit out of total 1326 combinations.
Therefore Probability of adjacent rank cards of same suit= (13*4)/1326 = 52/1326 = 0.0392.
5. Probability of being dealt on Ace, a pocket pair or a suited connector.
Probability of being dealt an Ace = 0.1447 (calculated above)
Probability of a pocket pair = 0.0588 (calculated above)
Probability of a suited connector = 0.0392 (calculated above)
Therefore probability of being dealt an Ace, a pocket pair or a suited connector = 0.1447 + 0.0588 + 0.0392 = 0.2427
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