Question 1133957: A group of 6 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.
The designated cards are: 7 of Spades, 5 of Hearts, Ace of Clubs. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.
What is the probability of a successful hand that will go all the way till everyone gets 7 cards?
Answer by Glaviolette(140)   (Show Source):
You can put this solution on YOUR website! You want 42 cards to not be the three indicated cards. The probability that the first card is not one of those three is 49/52, the probability that the second card isn't is 48/51, third card is 47/50, and so on until the 42nd cards isn't which would be 8/11. This calculates to be about .0054.
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