Question

Mark and job are basketball players and will play a game. In the game, Mark will get 2 free throw attempts and John will get three. Overall, Mark makes a basket on 90% of free throw attempts and John makes it 50% of the time. Mark will win the game if he makes more free throws than John. If it's a tie then John wins. Assuming independence. Let N denote the number of baskets made by Mark and S denote the number made by John.

What is the distribution and parameters for N and for S? What is the probability that Nash will win the game?