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?© BrainMass Inc. brainmass.com October 10, 2019, 3:44 am ad1c9bdddf
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 ...
The probability of obtaining a poker fullhouse is determined.