A local arcade is hosting a tournament in which contestants play an arcade game with possible scores ranging from 0 to 20. The arcade has set up multiple game tables so that all contestants can play the game at the same time; thus contestant scores are independent. Each contestant’s score will be recorded as he or she finishes, and the contestant with the highest score is the winner. After practicing the game many times, Josephine, one of the contestants, has established the probability distribution of her scores, shown in the table below. Crystal, another contestant, has also practiced many times. The probability distribution for her scores is shown in the table below. Calculate the expected score for each player. Suppose that Josephine scores 16 and Crystal scores 17. The difference (Josephine minus Crystal) of their scores is –1. List all combinations of possible scores for Josephine and Crystal that will produce a difference (Josephine minus Crystal) of –1, and calculate the probability for each combination. Find the probability that the difference (Josephine minus Crystal) in their scores is –1.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A local arcade is hosting a tournament in which contestants play an arcade game with possible scores
After practicing the game many times, Josephine, one of the contestants, has established the
Crystal, another contestant, has also practiced many times. The probability distribution for her scores is shown in the table below.
Calculate the expected score for each player.
Suppose that Josephine scores 16 and Crystal scores 17. The difference (Josephine minus Crystal) of their scores is –1. List all combinations of possible scores for Josephine and Crystal that will produce a difference (Josephine minus Crystal) of –1, and calculate the probability for each combination.
Find the probability that the difference (Josephine minus Crystal) in their scores is –1.
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