Question

It's estimated that 50% of e-mails are spam. A certain brand of software claims that it can detect 99% of spam mails and probability for a fakse positive thats the email is non-spam is 5%.Now an email is detected as spam.Then whats the probability that it's in fact a non-spam e-mail?​

Answer 1

Answer:

Let A denote the event that an email is detected as spam and B denote the event that an email is spam.

Given that 50% of the emails are spam, i.e., P(B)=0.5. Thus P(B′)=1−P(B)=0.50.

A certain brand of software claims that it can detect 99% of spam emails. That is P(A|B)=0.99.

And the probability for a false positive (a non-spam email detected as spam) is 5%. That is P(A|B′)=0.05.

We need to find the probability that the email is non-spam given that it is detected as spam.

Using Bayes' Theorem, required probability is