Question

(1) Two players are each dealt four cards. What is the probability that one of the two players is dealt exactly two aces, while the other player gets no aces?

(2) Two players are each dealt four cards. What is the probability that each player is dealt exactly one ace?

Answer 1

1

out of 52 cards we are dealing 4 consecutive cards to player 1, out of which two are Aces
P1(player 1 getting A, A, X, X) = (4/52)*(3/51)*(48/50)*(47/49) = 0.00417

now, out of remaining 48 cards, we are dealing 4 random cards other than Aces to player 2 (please note there are still 2 Aces in the remaining deck of 48 cards)
P2player 2 getting X, X, X, X) = (46/48)*(45/47)*(44/46)*(43/45) = 0.83865

Overall probability = P1 * P2 = 0.00417 * 0.83865 = 0.0035

2

we have to deal 1 Ace to each one

out of 52 cards we are dealing 4 consecutive cards to player 1, out of which one is Ace
P1(player 1 getting A, X, X, X) = (4/52)*(48/51)*(47/50)*(46/49) = 0.06388

now, out of remaining 48 cards, we are dealing 4 random cards to player 2 which will have 1 Ace (please note there are still 3 Aces in the remaining deck of 48 cards)
P2(player 2 getting A, X, X, X) = (3/48)*(45/47)*(44/46)*(43/45) = 0.0547

Overall Probability = 0.0035 * 0.0547 = 0.00019

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