5.118 Simulate table tennis In a table tennis game, the first person to get at least 11 points while being ahead of the opponent by at least two points wins the game. In games between you and an opponent, suppose successive points are independent and that the probability of your winning any given point is 0.45.

a. Do you have any reasonable chance to win a game?

Showing all steps, simulate two games by generating random numbers between 1 and 100; let numbers 1–45 represent winning a point and numbers 46–100 losing a point.

b. Combining results for all students in a class, estimate the probability of winning a game.