# you are "thinking right" :)

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Posted by Denis Borris on October 09, 2002 at 13:02:10:

In Reply to: I think you are right Mr. B... posted by Subhotosh Khan on October 09, 2002 at 11:02:46:

: : : : 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?
: : : *************************************
: : : Probability of drawing fist card (any) = 52/52
: : : Probability of drawing second card (same as first) = 3/51
: : : Probability of drawing third card (same as first) = 2/50
: : : Probability of drawing fourth card (same as first) = 3/49
: : : These are "mutually exclusive" events. Find combined probability.

: : The art of probability
: : Is sure not my forte.
: : SO in all PROBABILITY(!) a stupid question:
: : wouldn't the probability of getting 4-same simply be 13 / (all combos) ?
: ***************************************
: I see error in my ways.

: I was calculating chances of 4 of a kind on consecutive draw.

: Even at that the third line is wrong. It should be:

: Probability of drawing fourth card (same as first) = 1/49

: [that's what happens to lazy-bones trying to cut and paste]

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