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StatisticsProbability and Statistics for Engineering and the SciencesAt a certain gas station, 40% of the customers use regular gas ( A 1 ), 35% use plus gas ( A 2 ), and 25% use premium ( A 3 ). Of those customers using regular gas, only 30% fill their tanks (event B ). Of those customers using plus, 60% 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 2 ∩ 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? Plus? Premium?BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 2.4, Problem 59E

Textbook Problem

At a certain gas station, 40% of the customers use regular gas (*A*_{1}), 35% use plus gas (*A*_{2}), and 25% use premium (*A*_{3}). Of those customers using regular gas, only 30% fill their tanks (event *B*). Of those customers using plus, 60% 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*_{2}∩*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? Plus? Premium?

Expert Solution

**a.**

To determine

Find the probability that the customer requests plus gas and fill the tank

**Given info:**

The data consists of three types of gas in the gas station and has two methods to fill their tanks. The probability of the customers using regular gas is 40%, the probability of the customers using plus gas is 35%, and the probability of the customers using premium gas is 25%.

30% of customers fill the gas given that they use regular gas. 60% of customers fill the gas given that they use plus gas and 50% of customers fill the gas given that they use premium gas.

**Calculation:**

Here, *A* represents customers using the gas, *A _{1}* represents the customers using regular gas,

The probability that the customer requests regular gas and fill the tank is obtained as:

The probability that the customer requests plus gas and fill the tank is obtained as:

Expert Solution

**b.**

To determine

Find the probability that the customer fills the tank.

Expert Solution

**c.**

To determine

Find the probability that the customer requested regular gas.

Find the probability that the customer requested plus gas.

Find the probability that the customer requested premium gas.

Probability and Statistics for Engineering and the Sciences

Show all chapter solutions

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