The ACME Computer Co. operates three plants that manufacture notebook computers. The plants are located in Seattle, Singapore, and New York. The plants produce 20, 30, and 50 percent of the company's output, respectively. ACME attaches the labels "Seattle," "SING," or "NY" to the underside of the computer in order to identify the plant in which a notebook computer was manufactured. The computers carry a 2-year warranty, and if a customer requires repairs during the warranty period, he or she must send the computer back to the plant in which the computer was manufactured. There is also a stamp on the motherboard inside the computer which technicians at a plant can use as an additional way of identifying which plant manufactured the computer. The consumer is unable to examine this inside stamp, because if the consumer opens up the computer housing to look inside, a seal is broken which voids the warranty. Regarding quality control at the plants, the warrantyperiod failure rates of computers manufactured in the three plants are known to be \(.01, .05\), and .02 for the Seattle, Singapore, and New York plants, respectively. You have bought an ACME computer, and it has failed during the warranty period. You need to send the computer back to the plant for repairs, but the label on the underside of the computer has been lost and so you don't know which plant manufactured your computer.

a. Which plant is the most probable plant to have manufactured your computer?

b. Which plant is the least probable plant to have manufactured your computer?

c. What is the probability that an ACME notebook computer will fail during the warranty period?

d. Given that an ACME computer does not fail during the warranty period, what is the probability that the computer was manufactured in New York?