Problem 2.53 A new metal detector has been invented for detecting weapons in luggage. It is known that 1% of all luggage going through an airport contains a weapon. When a piece of luggage contains a weapon, an alarm (indicating a weapon is present) is activated 95% of the time. However, when the luggage does not contain a weapon the metal detector activates an alarm 10% of the time. Denote the event that a piece of luggage contains a weapon by W, the event that the alarm is activated by A+, and the event that the alarm is not activated by A−.

(a) A piece of luggage is selected at random and tested; what is the probability that the alarm is activated?

(b) Suppose the alarm is activated. Compute the probability that the piece of luggage actually contains a weapon.