At a certain gas station, 40% of customers use regular gas (A₁), 35% use plus gas (A₂), and 25% use premium (A₃). 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 tank.

a. What is the probability that the next customer will request plus 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? Plus? Premium?

Show me a vann diagram and all the necessary steps and details from scratch as much as possible please. Thank you.