Probability Poker Hand Full House

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We know that the probability of getting a full house is given by: P (Full house) = n (F)/n (S) n (S) = Number of elements in F = 52C5 = 2598960 In order to understand n (F), consider the following. Putting all of this together, we obtain the following ranking of poker hands: Poker Hand Number of Ways to Get This Probability of This Hand Royal Flush 4 0.000154% Straight Flush 36 0.00139% Four of a Kind 624 0.0240% Full House 3,744 0.144% Flush 5,108 0.197% Straight 10,200 0.392% Three of a Kind 54,912 2.11% Two Pairs 123,552 4.75% One Pair 1,098,240 42.3% Nothing 1,302,540 50.1% Wait, how did I compute the probability of getting “Nothing”?

  1. Probability Poker Hand Full House Images
  2. Probability Poker Hand Full House Or Flush Who Wins
  3. Probability Poker Hand Full House
  4. Probability Poker Hand Full House Rankings

A game of poker is played with an ordinary deck of 52 cards, and each player is dealt a hand of 5 cards chosen at random. What is the probability that a player will be dealt a full house, given that the first two cards they get are of the same denomination?

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https://brainmass.com/math/probability/probability-poker-fullhouse-433206

Solution Preview

Given that we get two cards of the same denomination (let's say they are Xs), there are two possibilities,

1) The triple of the full house is that number (i.e. we have a triple X) and another pair (say a pair of Y), OR
2) The pair of the full house is the two cards we just got (i.e. a pair of Y and a triple X).

Let's consider case 2) first,

There are 50 cards left, and 2 of them are X (since we got 2 Xs already). Our third card ...

Solution Summary

The probability of obtaining a poker fullhouse is determined.

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Find the probability of getting the following hands in a game of traditional 5 card poker.

(1)) P(Having exactly 2 Aces) (other 3 cards can be anything but aces)
The probability is (displaystylefrac{103,776}{2,598,960} approx 3.9930%)


(2)) P(Royal Flush) (aka 10, J, Q, K, A and all the same suit)

Probability Poker Hand Full House Images

The probability is (displaystylefrac{4}{2,598,960} approx 0.000154%)
(3)) P(Straight Flush) (aka same suit, in consecutive number order)
The probability is (displaystylefrac{36}{2,598,960} 0.00139approx 0.00139%)
(4)) P(Flush) (aka all cards in the same suit.)
The probability is (displaystylefrac{624}{2,598,960} approx 0.0240%)

Probability Poker Hand Full House Or Flush Who Wins

(5)) P(Straight) (aka all cards in consecutive number order.)
The probability is (displaystylefrac{3,744}{2,598,960} approx 0.1441%)
(6)) P(Full house) (aka 3 of a kind and a pair)
The probability is (displaystylefrac{5,108}{2,598,960} approx 0.1965%)
(7)) P(Four of a kind)
The probability is (displaystylefrac{10,200}{2,598,960} approx 0.3925%)
(8)) P(Three of a kind)
The probability is (displaystylefrac{54,912}{2,598,960} approx 2.1128%)
(9)) P(Two pair)
The probability is (displaystylefrac{123,552}{2,598,960} approx 4.7539%)
(10)) P(One Pair)
The probability is (displaystylefrac{1,098,240}{2,598,960} approx 42.2569%)
(11)) P(No pair)Poker
The probability is (displaystylefrac{1,302,540}{2,598,960} approx 50.1177%)

Probability Poker Hand Full House


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