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probability of card dealing
Posted:
Jan 30, 2014 3:15 PM
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Trying to compute the probability of an opponent being dealt a specified pair (two cards) from an initially well-shuffled (uniform distribution) 52-card deck, given that I know the two cards I've been dealt already, in a two-person 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 Ace-King (of any suit combo), given that I know I have Ace-King in my hand already?
My idea of how to do this is to use Bayes' formula
P(X+Y) = P(X|Y)P(Y)
where
+ here indicates the union
and the events are
X = opponent's hand is Ace-King pair
Y = my hand is Ace-King pair
Then P(Y) = 16/1326 = 0.0121
16 = # ways to get an Ace-King pair
1326 = # two card combinations (unordered) from 52-card deck
P(X|Y) = 9/1225 = 0.0073
9 = # remaining ways to get Ace-King pair, since one Ace and one King are already in my hand
1225 = # two card combos from remaining 50-card deck
Then
P(X+Y) = 0.0073*0.0121 = 8.89e-5 or 0.89%
Is this correct? Thank you.
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