. At a certain gas station, 40% of the customers use regular gas (A1), 35% use mid-grade gas (A2), and 25% use premium gas (A3). Of those customers using regular gas, only 30% fill their tanks (event...

. At a certain gas station, 40% of the customers use regular gas (A1), 35% use mid-grade gas (A2),

and 25% use premium gas (A3). Of those customers using regular gas, only 30% fill their tanks

(event B). Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using

premium, 50% fill their tanks.

(a) What is the probability that the next customer will request mid-grade gas and fill the tank

(A2 \ 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?

mid-grade gas? Premium gas?