A three dice roll question I got this question from an interview.
A and B are playing a game of dice as follows. A throws two dice and B throws a single die. A wins if the maximum of the two numbers is greater than the throw of B. What is the probability for A to win the game?
My solution.
If $(X,Y)$ are the two random throws of A and $Z$ is the random throw of B, then the problem asks (if I guessed correctly) to compute $P(\max(X,Y)>Z)$. But how to do it? I highly appreciate your help.

Since this is an interview question, simple thinking and an approximate answer is best. Three dice are thrown, the biggest number wins. The probability to win is $1/3$ for each of the die. Player A has two dice, and so wins in $2/3$ of the cases. Done.
This is a slight over-estimate since whenever player B throws a 6, player B automatically wins. Other answers give ideas on how to calculate more accurately. But somehow that's not so much fun, is it.
