Consideranemailserverequippedwithaspamflaggingsoftware.Thefollowing

information is known.

(a)The probability that an incoming email is flagged as a spam is 0.1.

(b)Provided that an income message is flagged as a spam, the probability that it is actually a

spam is 0.9

Basedontheaboveinformation,pleaseanswerthefollowingquestions.

(a)Assume that an income message is a spam.What is the lowest possible probability

that it is flagged as a spam

(b)Assume that an income message is genuine.What is the lowest possible probability that it

is flagged as a spam?

Hint:In both questions, you need to consider the messages that are not flagged as a

spam and to determine which percentage of them must be a spam.