Problem# Question B (not in the book) A spam-detection filter is tested on 100 e

Question

Problem# Question B (not in the book) A spam-detection filter is tested on 100 emails that are truly spam, and it flags 78 of them as spam and the others it lets slip by. It's also tested on 1000 emails that are not spam, and it properly lets 950 of them through, flagging only 50 as spam. Suppose that in general, 40% of emails are spam. If an email from this general pool is flagged as spam, what is the probability it's actually spam? Here's some space for work: Answer: Probability it's actually spam = Problem# Question B (not in the book) A spam-detection filter is tested on 100 emails that are truly spam, and it flags 78 of them as spam and the others it lets slip by. It's also tested on 1000 emails that are not spam, and it properly lets 950 of them through, flagging only 50 as spam. Suppose that in general, 40% of emails are spam. If an email from this general pool is flagged as spam, what is the probability it's actually spam? Here's some space for work: Answer: Probability it's actually spam =

Explanation / Answer

P(P|S) = 0.78 and P(P'|S) = 0.22
P(P|S') = 0.05 and P(P'|S') = 0.95
P(S) = 0.4 and P(S') = 0.6

Probability that an email is actual spam,
P(S|P) = P(P|S)*P(S) / (P(P|S)*P(S) + P(P|S')*P(S'))

P(S|P) = 0.78*0.4 / (0.78*0.4 + 0.05*0.6) = 0.9123

Probability it's actually spam = 0.9123

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