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% filltheir tanks (event B). Of those customers using plus, 60% fill their tanks, whereas ofthose using premium, 50% fill their tanks. (a) What is the probability that the next customer will request plus gas and fill thetank ? (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 isrequested?

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.)

According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year.  Consider two randomly selected Americans and assume that these two randomly selected Americans are independent of each other.  The probability that neither of these two randomly selected Americans will contract the influenza virus in a given year is

A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?