3. (10 pts) Suppose that 15% of spam messages that you receive contain the word

Question

3. (10 pts) Suppose that 15% of spam messages that you receive contain the word "greeting" and 1% of non-spam messages that you receive contain the word "greeting." Also suppose that 25% of the messages that you receive are spam. Consider selecting one of your email messages at random, and define the following events: G = {message contains the word "greeting"), M- message is spam. b) (4 pts) Determine the probability that a randomly selected e-mail message contains the word "greeting" and is a spam. e4pts etermine the probability that a randomly selected e-mail message contains the word "greeting" and is not a spam.

Explanation / Answer

Ans:

Given that

P(greeting/spam)=P(G/M)=0.15

P(greeting/non spam)=P(G/Mc)=0.01

P(spam)=P(M)=0.25

P(non spam)=P(Mc)=1-0.25=0.75

b)P(G and M)=P(G/M)*P(M)=0.15*0.25=0.0375

c)P(G and Mc)=P(G/Mc)*P(Mc)=0.01*0.75=0.0075

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