A list of poker hands ranked in order from the highest to th

A list of poker hands, ranked in order from the highest to the lowest, ?s shown in the accompanying table along with a description and example of each hand. Use the table to help you answer the question. If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? (Round your answer to five decimal places.) Four of a kind

Solution

Since there are 13 ranks in a set of card, there can be 13 sets of 4 cards of same rank.

Therefore, P(Four of a kind) = P(4 cards of same rank) x 13

Now, P(4 cards of any particular rank, say K) = Probability of K at 1st draw from 52 cards x Probability of K at 2nd draw from the remaining 51 cards x Probability of K at 3rd draw from the remaining 50 cards x Probability of K at 4th draw from the remaining 49 cards = 4/52 x 3/51 x 2/50 x 1/49

Therefore, P(Four of a kind) = 4/52 x 3/51 x 2/50 x 1/49 x 13 = 0.00005