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A poker hand is defined as drawing 5 cards at random
Chapter 1, Problem 17E(choose chapter or problem)
PROBLEM 17E
A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of each of the following poker hands:
(a) Four of a kind (four cards of equal face value and one card of a different value).
(b) Full house (one pair and one triple of cards with equal face value).
(c) Three of a kind (three equal face values plus two cards of different values).
(d) Two pairs (two pairs of equal face value plus one card of a different value).
(e) One pair (one pair of equal face value plus three cards of different values).
Questions & Answers
QUESTION:
PROBLEM 17E
A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. Find the probability of each of the following poker hands:
(a) Four of a kind (four cards of equal face value and one card of a different value).
(b) Full house (one pair and one triple of cards with equal face value).
(c) Three of a kind (three equal face values plus two cards of different values).
(d) Two pairs (two pairs of equal face value plus one card of a different value).
(e) One pair (one pair of equal face value plus three cards of different values).
ANSWER:
Answer :
Step 1 of 5 :
Given, A poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards.
The claim is to find the probability four of a kind ( four cards of equal face value and one card of a different value.)
The total number of ways different poker hand can be possible =
The number of ways when four of a kind =
=
Therefore, P(four of a kind) =
=
=
= 0.0002400.