Final answer:
The correct distribution to model this scenario is the binomial distribution.
Step-by-step explanation:
In this scenario, the players' probability ends when one player wins n games. This means that the game stops when a player reaches a certain number of wins. We need to determine the distribution that can model this situation.
A) Geometric distribution: The geometric distribution is used to model the number of trials needed to achieve the first success. Since we want to stop when a player wins n games, the geometric distribution is not appropriate for this scenario.
B) Binomial distribution: The binomial distribution is used to model the number of successes in a fixed number of independent trials. In this case, each game is an independent trial and the goal is to reach n wins, so the binomial distribution is appropriate.
C) Poisson distribution: The Poisson distribution is used to model the number of events occurring in a fixed interval of time. It is not suitable for this scenario as we are interested in the number of games played until a player wins n games.
D) Uniform distribution: The uniform distribution is used to model outcomes that have equal probability. Since the probability of winning a game is not constant, but rather determined by the player's performance, the uniform distribution is not applicable.
Therefore, the correct answer is B) Binomial distribution.