Question

Naina receives emails that consists of 18% spam of those emails. The spam filter is 93% reliable i.e., 93% of the mails it marks as spam are actually a spam and 93% of spam mails are correctly labelled as spam. If a mail marked spam by her spam filter, determine the probability that it is really spam.

(a) 50%

(b) 84%

(c) 39%

(d) 63%

The question was asked during an interview.

This key question is from Discrete Probability in portion Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (a) 50%

Best explanation: 18% email are spam and 82% email are not spam. Now, 18% of mail marked as spam is spam and 82% mail marked as spam are not spam. By Bayes theorem the probability that a mail marked spam is really a spam = (Probability of being spam and being detected as spam)/(Probability of being detected as spam)  = (0.18 * 0.82)/(0.18 * 0.82) + (0.18 * 0.82) = 0.5 or 50%.