At a certain gas station, 40% of the customers use regular gas (A,), 35% use plus gas (A,), and 25% use premium (A,). Of those customers using regular gas, only 20% fill their tanks (event B). Of those customers using plus, 40% fill their tanks, whereas of those using premium, 50% fill their tanks. (a) What is the probability that the next customer will request plus gas and fill the tank (A, n B)? (b) What is the probability that the next customer fills the tank? (c) If the next customer fills the tank, what is the probability that regular gas is requested? (Round your answer to three decimal places.) If the next customer fills the tank, what is the probability that plus gas is requested? (Round your answer to three decimal places.) If the next customer fills the tank, what is the probability that premium gas is requested? (Round your answer to three decimal places.)

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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.