Suppose that 15% of spam messages that you receive contain the word “greeting” a

Question

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.

a.)Produce a table of 1000 hypothetical e-mail messages, classified according to (whether or not the message is spam) and (whether or not the message contains the word “greeting”).

b.)According to the given percentages, what percentage of e-mail messages that you receive contain the word “greeting”?

c.)Given that a randomly selected e-mail message contains the word “greeting,” what is the probability that the message is spam?

Explanation / Answer

Ans:

a)0.15*250=37.5,but rounded to 38

b)P(greeting)=45/1000=0.045 or 4.5%

c)P(spam/greeting)=P(greeting and spam)/Pgreeting)=38/45=0.844

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