Question

If a poker hand (five cards) is known to contain at least three
aces, what is the probability that it contains all four aces?

Answer 1

I think you should use the definition of conditional probability.

Answer 2

P(have all four aces| hand contains at least three aces)

=P(have all four aces,hand contains at least three aces)/P(hand contains at least three aces)

=P(have all four aces)/P(hand contains at least three aces)

Answer 3

let A=#aces

=P(A=4)/P(A>=3)=P(A=4)/[P(A=3)+P(A=4)]

Answer 4

Zarkon, you are correct
i thought i could take a shortcut but you get a different answer

i believe you should get 48/4560 = 1/95

Answer 5

\[P(A=4)=\frac{_{4}C_4\cdot_{48}C_{1}}{_{52}C_5}\]

\[P(A=3)=\frac{ _{4}C_3\cdot_{48}C_{2}}{_{52}C_5}\]

Answer 6

1/95 is correct