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

Naina receives emails that consists of 18% spam of those emails. The s

1.	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» 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%.

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