Probability Question 392
Question: What is the probability of getting a FULL HOUSE in five cards drawn in a pork game from a standard pack of 52-cards? [A FULL HOUSE consists of 3 cards of the same kind (e.g. 3 Kings) and 2 cards of another kind (e.g. 2 aces)]
Options:
A) $ \frac{6}{4165} $
B) $ \frac{4}{4165} $
C) $ \frac{3}{4165} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
There are 6 ways to select 2 cards of the same kind from the 4 cards in the deck and there are 13 different kinds of cards, so the total number of combinations possible of 2 cards is $ 6\times 13=78. $
There are 4 ways to choose 3 cards of the same kind from 4 cards of the same kind, but because the 3-of a-king suit must be different from the 2-of -a-kind suit, the possible combinations of this is, $ 4\times 12=48. $
So total number of ways is $ =48\times 78=3744 $ Sample space is $ ^{52}C_5=2,598,560 $
Required probability $ =\frac{3744}{2598560}=\frac{6}{4165} $
BETA
