Answer to Question #10306 in Statistics and Probability for Raghav Agrawal

Question

You are playing Texas Hold ‘em. For your two card hand, you receive an Ace and a King. This is a good hand to start with, and there are many ways it can become a very good hand. In particular, you can make three-of a kind, where the cards dealt on the board include two kings or two aces, making three total, including the ones in your hand.
a. What is the probability that there are exactly two kings dealt on the flop? That is, what is the probability that two kings are amongst the first three cards dealt?
b. Given your answer to a, what is the probability that there are two kings or two aces on the flop?

Answer 1

a)

3/50*47/49*46/48*3! 
where 3/50 - probability of king, 
47/49 - probability of another (second) card 
And 46/49 – probability of a third one. 
3! – permutations 

b)

it is P(2kings)+P(2aces)- P(2kings &&2 aces)= 3/50*44/59*43/48*3!+ 3/50*44/49*43/48*3!-

- 3/50*3/49*44/48*3!=0.509