Probability in a card game

[truewt]

Hi guys.

A question came to me as I'm playing a card game with 4 players. Let's say the full deck (of 52 playing cards) are all dealt to each player, one at a time into player's hands in a direction. All the cards are fully dealt before a player views the cards in his hands.

Assume player Z picks up his hand and takes a look at the first 3 cards. They are all Aces. What will the probability of player Z having the 4th Ace in the rest of his hands (assuming he didn't see the rest of them). Will it be conditional probability, or will the probability be equivalent to that of player Z holding all 4 Aces, regardless of him looking at the first 3 cards or not?

And what will be the solution to the probability be like? Sorry I wanted to attempt at this problem, but seems that there's also this chance that the other players get an Ace, hence it would be incorrect to say the probability of getting the 4 Aces is that simple?

 

[mathman]

Assume player Z picks up his hand and takes a look at the first 3 cards. They are all Aces. What will the probability of player Z having the 4th Ace in the rest of his hands (assuming he didn't see the rest of them). Will it be conditional probability, or will the probability be equivalent to that of player Z holding all 4 Aces, regardless of him looking at the first 3 cards or not?

Since Z has 3 aces, the probability of having the fourth ace is 10/49. This is much higher than the probability of having all four aces sight unseen.