# Re: Poker Problem - 10/08/02

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Posted by Paul on October 15, 2002 at 00:30:06:

Posted by Paul on October 08, 2002 at 16:05:00:

A poker had of 5 cards is drawn from standard 52 card deck w/o replacement.
What is the probability we get 4 cards of one kind?

If do not get 4 of a kind on 1st draw, we keep the highest for which we have several of a kind (if none, keep only the highest card) then throw away the others and replace w/fresh cards. Can only do this once.What is the probability we get 4 of a kind if we follow this strategy?
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could someone tell me if im on the right track for the 2nd part of the prob

there would be 4 cases where you'd get 4 of a kind on next draw
1) Keep the highest card from 1st draw, then get 4 cards of same kind on next draw (eg. card you kept was a Queen, then u drew 4 aces)
2) Keep the highest card, then get 3 cards same as one you kept and 1 other card
3) Keep highest pair, then get 2 cards same as pair you kept and 1 other card
4) Keep triple, get remaining card same as triple and 1 other card

i worked of the probability of the 4 cases
so would the probability of getting 4 of a kind using the stratgegy
be the sum of the 4 probabilities above?
or would i have consider that i didnt get 4 of a kind on the 1st draw?
if so, how would i incorporate that into the answer?

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