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In a game of poker, what is the probability that a
Chapter , Problem 13(choose chapter or problem)
In a game of poker, what is the probability that a five-card hand will contain (a) a straight (five cards in unbroken numerical sequence), (b) four of a kind, and (c) a full house (three cards of one value and two cards of another value)?
Questions & Answers
QUESTION:
In a game of poker, what is the probability that a five-card hand will contain (a) a straight (five cards in unbroken numerical sequence), (b) four of a kind, and (c) a full house (three cards of one value and two cards of another value)?
ANSWER:Step 1 of 4
The number of ways that a five-card can be taken in 52 -cards is, .
In 9 ways you can take a straight. But "Ace" is considered as a small number in some games and a big number in some games.
Then can take a straight in 10 ways. If select a straight five cards,
First card can be taken in 4 ways, the second card can be taken in 4 ways, the third card can be taken in 4 ways, the fourth card can be taken in 4 ways and the fifth card can be taken in 4 ways.
Therefore, total number of ways are .
Since, it needs a straight 5 cards in unbroken numerical sequence, Discard Ace, Knave, Jack, Queen. These are 4.
To select a straight 5 cards in unbroken numerical sequence is, .
Therefore, total number of ways are .