Answer: 0.144%
Explanation:
To find the probability of getting a full house, we can divide the number of ways to get a full house by the total number of possible hands.
There are (52 choose 5) total possible hands of 5 cards from a deck of 52 cards.
To get a full house, we first need to choose the rank of the 3 cards that will be the same. There are 13 ranks to choose from, so there are (13 choose 1) ways to do this.
Once we have chosen the rank for the 3 cards, we need to choose which 3 of the 4 cards of that rank we will use. There are (4 choose 3) ways to do this.
Next, we need to choose the rank of the 2 cards that will be the same. There are now 12 ranks left to choose from, so there are (12 choose 1) ways to do this.
Finally, we need to choose which 2 of the 4 cards of that rank we will use. There are (4 choose 2) ways to do this.
So the total number of ways to get a full house is:
(13 choose 1) * (4 choose 3) * (12 choose 1) * (4 choose 2) = 13 * 4 * 12 * 6 = 3,744
Therefore, the probability of getting a full house is:
3,744 / (52 choose 5) = 0.00144057623
So the probability of getting a full house is approximately 0.00144057623, or about 0.144%.