Problem #2 (Total 9 points) 3 points (i) 3 points (!!) 3 points (iii) At a certain gas station, 40% of the customers use regular gas (call this event A1), 35% of the customers use plus gas (A2), and 25% use premium gas (A3). Let B denote the event that a customer fills tank. Of those who fill regular gas only 35% fill their tanks i.e., P(B|A1)=0.35. Of those using plus gas, 70% fill their tanks, whereas those using premium, 50% fill their tanks. What is the probability that a customer will fill tank and use regular gas i.e., P(BnA1)? What is the probability that a customer fills tank P(B)? If a customer fills her tank, what is the probability she has selected premium gas i.e., P(A3|B)?