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 ofyour email messages at random, and define the following events: G message contains the word "greeting"), M message is spam a) (2 pts) Express the given values.15,.01, and .25 as probabilities in terms of these events. b) (4 pts) Determine the probability that a randomly selected e-mail message contains the word "greeting" and is a spam. c) (4 pts) Determine t word "greeting" and is not a spam. he probability that a randomly selected e-mail message contains the

Explanation / Answer

a) P(G|M) =0.15 ; P(G|Mc) =0.01

P(M)= 0.25

b) P(G n M) =P(M)*P(G|M) =0.25*0.15 =0.0375

c)

P(G n Mc) =P(Mc)*P(G|Mc) =0.75*0.01 =0.0075

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