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Find the probability of a full house in a poker hand
Full house = 3 cards of the same face value + 2 cards of the same face value
Full house = 3 cards of the same face value + 2 cards of the same face value
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27 Nov 2005, 19:22
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Probability of getting 4 A's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 2's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 3's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 4's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 5's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 6's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 7's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 8's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 9's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 10's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 J's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 Q's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 K's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
In sum, 1/1199520 * 13 = 13/1199520
*************************************
Since 1199520 doesn't look beautiful, I guess I'm wrong again...
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 2's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 3's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 4's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 5's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 6's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 7's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 8's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 9's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 10's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 J's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 Q's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
Probability of getting 4 K's and 1 other card.
= 1/51 * 1/50 * 1/49 * 1/48 * 5
= 1/1199520
In sum, 1/1199520 * 13 = 13/1199520
*************************************
Since 1199520 doesn't look beautiful, I guess I'm wrong again...
