In the game of poker, five cards from a standard deck of 52 cards are dealt to each player.
Assume there are four players and the cards are dealt five at a time around the table until all four players have received five cards.
a. What is the probability of the first player receiving a royal flush (the ace, king, queen, jack, and 10 of the same suit).
b. What is the probability of the second player receiving a royal flush?
c. If the cards are dealt one at a time to each player in turn, what is the probability of the first player receiving a royal flush?
I know that the probability of a royal flush is 1649740, because of 52C5=2598960, and 42598960=1649740.
But I am struggling to understand how to determine the probability of the first player getting it, etc…
Any help would be greatly appreciated.
Best Answer
The important point is that all three probabilities are the same. It is easy to confuse yourself on b thinking that the cards removed for the first player change the probability for the second player. They do if you know what they are, but if you do not they do not change anything. For b, think about doing exactly what is described, they having the two players exchange hands. Now what is the chance the second player has a royal flush? For c you are just pulling cards from different locations in the deck. If the deck is well shuffled, that does not matter.