Steven Nash and Shaquille O'Neal are basketball players and will play a game. In the game, Nash will get 2 free throw attempts and O'Neal will get 3 free throw attempts. Overall, Nash makes a basket on 90% of free throw attempts, O'Neal makes a basket on 50% of his free throw attempts. Nash will win the game if he makes more baskets on the free throws than O'Neal (if they tie with the same number of baskets, O'Neal wins the game). We will assume independence between the players and the attempts. Let N denote the number of baskets made by Nash and S denote the number of baskets made by O'Neal.
a) What is the distribution and parameter(s) for N and for S?
b) What is the probability that Nash will win the game?
c) Suppose that they play the game (as described above) 10 times, what is the probability that Nash will win 4 times? (hint: use the information you found in part b)
d) Suppose that they play the game (as described above) 10 times, how many games does Nash expect to win?
e) Suppose that they play the game (as described above) 10 times, what is the probability that O'Neal first win is in the second game?