(Devore: Section 2.4 #59) At a certain gas station, 40% of the 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 tanks. (a) What is the probability that the next customer will request plus gas and fill the tank (A₂B)? (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?

A manufacturing process​ produces, on the​ average, 3​% defective items. The company ships 15 items in each box and wishes to guarantee no more than 1 defective item per box. If this guarantee accompanies each​ box, what is the probability that the box will fail to satisfy the​ guarantee?

A company buys microchips from three suppliers I, II and III. Supplier I has a record of providing microchips that contain 10% defective; supplier a defective rate of 5% and supplier III has a defective rate of 3%. Suppose 10%, 40% and 50% of the current supply came from suppliers I, II and III, respectively. If a randomly selected microchip is defective, what is the probability that it came from supplier II? Express your answer accurate to two decimal places. O 48 O..40 O something else O 44 O 41

At a certain gas station, 40% of the customers use regular gas (A₁), 35% use plus gas (A₂), and 25% use premium (A3). 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, 70% fill their tanks. (a) What is the probability that the next customer will request plus gas and fill the tank (A₂ 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.)