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). Ofthose 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.)

Name: At a certain gas station, 40% of the customers use regular gas (A,),
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Description: 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). Ofthose customers using plus, 40% fill their tanks, wher

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MATLAB: An Introduction with Applications

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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.)

Expert Solution

Step 1

Given information:

Percentage of customers using regular gas, $P (A_{1}) = 0.40$

Percentage of customers using plus gas, $P (A_{2}) = 0.35$

Percentage of customers using premium gas, $P (A_{3}) = 0.25$

Percentage of customers filling their tanks out of those who use regular gas, $P (B | A_{1}) = 0.20$

Percentage of customers filling theire tanks out of those who use plus gas, $P (B | A_{2}) = 0.40$

Percentage of customers filling their tanks out of those who use premium gas, $P (B | A_{3}) = 0.50$

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