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probability of card dealing
Posted:
Jan 30, 2014 3:15 PM


Trying to compute the probability of an opponent being dealt a specified pair (two cards) from an initially wellshuffled (uniform distribution) 52card deck, given that I know the two cards I've been dealt already, in a twoperson game. To clarify, each player is dealt only two cards, face down (but I can look at mine).
For example, What is probability that my opponent receives AceKing (of any suit combo), given that I know I have AceKing in my hand already?
My idea of how to do this is to use Bayes' formula P(X+Y) = P(XY)P(Y) where + here indicates the union and the events are X = opponent's hand is AceKing pair Y = my hand is AceKing pair
Then P(Y) = 16/1326 = 0.0121 16 = # ways to get an AceKing pair 1326 = # two card combinations (unordered) from 52card deck
P(XY) = 9/1225 = 0.0073 9 = # remaining ways to get AceKing pair, since one Ace and one King are already in my hand 1225 = # two card combos from remaining 50card deck
Then P(X+Y) = 0.0073*0.0121 = 8.89e5 or 0.89%
Is this correct? Thank you.



