Recall that a standard 52-card deck has 4 suits, namely ♥, ♦, ♣, and ♠, each of which has 13 cards of different kinds or ranks, namely A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, and 2. One infamous five-card hand is the Dead Man’s Hand, consisting of A♣, A♠, 8♣, 8♠, and Q♥. According to legend – there seem to be no contemporary accounts that describe the hand – this is the poker hand that James Butler “Wild Bill” Hickok held when he was shot in the back of the head in a saloon in the town of Deadwood in the then Dakota Territory in 1876. 1. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will be the Dead Man’s Hand? 2. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have no card in common with the Dead Man’s Hand? 3. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have exactly one card in common with the Dead Man’s Hand? 4. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have at least one card in common with the Dead Man’s Hand?
Q. Recall that a standard 52-card deck has 4 suits, namely ♥, ♦, ♣, and ♠, each of which has 13 cards of different kinds or ranks, namely A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, and 2.
One infamous five-card hand is the Dead Man’s Hand, consisting of A♣, A♠, 8♣, 8♠, and Q♥. According to legend – there seem to be no contemporary accounts that describe the hand – this is the poker hand that James Butler “Wild Bill” Hickok held when he was shot in the back of the head in a saloon in the town of Deadwood in the then Dakota Territory in 1876.
1. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will be the Dead Man’s Hand?
2. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have no card in common with the Dead Man’s Hand?
3. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have exactly one card in common with the Dead Man’s Hand?
4. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have at least one card in common with the Dead Man’s Hand?
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