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