A busy hospital in a metropolitan area is considering installing a new device that would detect whether someone entering the hospital has a fever or not. Preliminary tests show that the device would correctly identify someone who has a fever with 95% probability and correctly identify someone who doesn't have a fever with 90% probability. Assume that there is a 10% chance that someone who enters the hospital has a fever.

a) If the device indicates that a person has a fever, what is the probability that the person actually has a fever?

b) If the device indicates that a person does not have a fever, what is the probability that the person actually does not have a fever?