An auto manufacturer has studied the choice of options available to customers when ordering a new vehicle. of the customers who order a car, 15% choose a sunroof, 40% choose a leather interior, 10% choose both, and the rest opt for neithert Of the customers who order a truck, 30% choose an extended cab, 40% choose all-wheel drive, 20% choose both, and the rest opt for neither. You cannot get a sunroof on a truck or an extended cab on a car. For this brand, half of the customers who order a vehicle choose a car. (a) Organize these probabilities as a probability tree. (b) What's the probability that the customer orders a vehicle with a sunroof? (a) Complete the probability treet Car and Sunroof Car and Leather Interior Car Car and Bath Car and Neither Truck and Extended Cab Truck and All-Wheel Drive Truck Truck and Bath Truck and Neither (Type integers or decimals) A vendor specializing in outdoor gear offers customers three ways to place orders for home delivery Customers can place orders either in the store, online, or via telephone using a catalog Of the orders, three-quarters are made online with one-eighth each made in stores or via telephone. Of the online orders, 30% are only for clothing, 30% are only for camping supplies, and 40% are for both. For orders placed in the store, all are for clothing (to order a size that is not in stock), Among orders placed via telephone, 50% are only for clothing, 20% are only for camping supplies, and 30% are for both. Answer parts (a) and (b). (a) Organize these probabilities as a probability table. Purchase Method On-Llne In Store Telephone Total | Clothing Purchase Camplng Both Total (Simplify your answers, Type integers or decimals.) Some electronic devices are better used than new. The failure rate is higher when they are new than when they are six months old. For example, half of the personal music players sold by a particular brand have a aw. If the player has the aw, it dies in the rst six months, If it does not have this aw, then only 10% fail in the rst six months. Yours dies after you had it for three months' What are the chances that it has this aw? The probability that it has the aw is . (Round to three decimal places as needed.) Some of the managers at a company have an MBA degree. of managers at the level of director or higher, 57% have an MBA. Among other managers of lower rank, 35% have an MBA. For this company. 17% of managers have a position at the level of director or higher If you meet an MBA from this rm, what are the chances that this person is a director (or higher)? The probability the person is a director or higher given that they have an MBA is (Round to three decimal places as needed)