(20 points) At a certain gas station, 40% of the customers use regular unleaded gas (A₁), 35% use extra unleaded gas (A₂), and 25% use premium unleaded gas (A3). Of those using regular gas, only 30% fill their tanks (event B). Of those customers using extra gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. What are the simple events in this scenario? b. What is the relationship between the simple events? Explain. C. Draw a diagram that illustrates the relationship. Label the probabilities and events. d. Find the probability that the next customer will request regular unleaded gas and fill the tank. e. Find the probability that the next customer fills the tank.
