Question

Suppose that 15 percent of the messages arriving at a mailxbox are spam and that 20 percent
of spam messages arriving there contain the word “winner”. Suppose also that the probability
that the word “winner” appears in a non-spam message is 5 percent.
(a) What percentage of the received emails contain the word “winner”?
(b) Suppose that a message is tagged as spam based on containing the word “winner”. Find
the probability that the message is indeed a spam.

Answer 1

a)let suppose there are 100 mailbox massages. out of them only 15 are spam and 85 are non spam. among 15 non spam there are 15*20%=3 are winner and among 85 there are 85*5%=4.25 are winner then total winner massages are =(3+4.25)=7.25

then 7.25% are winner massages.

b)

subposse Sidenote spam Widenate winners, Then p osto 1631) P(S1w) - P(WIS) PCS). P(N/ ) P($)+ PCH/99 P(89) 0.20 X 0.195 0. 20 X0.15+ 0.0 5X 0.895 in 0.414