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

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) The probability of player winning the game depends on the skill level . If  skill level increases the probability to win also increases. The probability of success (win) must remain constant for every trial (condition of binomial distribution), hence, this case cannot be modeled by a random binomial probability.

(B) Different skill levels means the probability of success differs between players, the probability of winning each game would differ between players,  hence. X can not be a binomial random variable.

(C) Same explanation as B  

(D) As both players have same skill set throughout the game, the probability of winning each of the n = 100 games is the cosnat; hence, X can be modeled as a binomial random variable

(E) Same explanation as B and C  

step-by-step explanation: