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 90% of the time. However, when the luggage does not contain a weapon the metal detector activates an alarm 10% of the time.

a)A piece of luggage is selected at random and tested. What is the probability that the alarm is not activated?

b)Suppose the alarm is not activated. Compute the probability that the piece of luggage actually contains a weapon.

c)Are the events "containing a weapon" and "alarm is not activated" independent? (You must show computations to support your answer)

d)Are the events "containing a weapon " and "alarm is not activated" mutually exclusive (disjoint)? (You must show computations to support your answer)