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vfiekz [6]
3 years ago
6

A popular computer card game keeps track of the number of games played and the number of games won on that computer. The cards a

re shuffled before each game, so the outcome of the game is independent from one game to the next and is based on the skill of the player. Let X represent the number of games that have been won out of 100 games. Under which of the following situations would X be a binomial random variable?
(A) All games were played by the same player, whose skill improved over the course of the 100 games.
(B) A group of 5 players of different skill levels were each allowed to play 20 games in a row.
(C) A group of players of different skill levels were each allowed to play until they had lost 3 games and this resulted in 100 games played.
(D) Two players of equal skill level each played from day to day. game a day for 50 days and their skill level did not change one.
(E) Two players of different skill levels competed by allowing one player to continue until a game was lost, then the other player to continue until a game was lost, and so on, until 100 games were played.
Mathematics
1 answer:
kari74 [83]3 years ago
5 0

Answer:

(D) Two players of equal skill level each played one game a day for 50 days and their skill level did not change from day to day.

Step-by-step explanation:

(A) If the player's skill improves over time, the likelihood of him winning the game also increases and, therefore, this scenario cannot be modeled by a random binomial probability.

(B) Since the players have different skill levels, the likelihood of winning each game would change between players, thus X is not a binomial random variable.

(C) Same explanation as alternative B  

(D) Since both players have the same constant skill level throughout all games, the likelihood of winning each of the 100 games is the same; therefore, X is a binomial random variable

(E) Same explanation as alternatives B and C  

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