Question

It is estimated that 50% of emails are spam emails. Some software has beenapplied to filter these spam emails before they reach your inbox. A certain brandof software claims that it can detect 99% of spam emails, and the probabilityfor a false positive (a non-spam email detected as spam) is 5%.Now if an email is detected as spam, then what is the probability that it isin fact a non-spam email?

Answer 1

Answer:

P(Non-Spam/Spam Detected) = 5/99

Step-by-step explanation:

To determine the probability that it is in fact a non-spam email, we will employ the use of Bayes Theorem: P(A/B) = (P(B/A) x P(A)) / P(B).

P(Spam) = P(Non-Spam) = 0.5  

P(Spam Detected) = P(Spam) * rate of detection = 0.5 * 0.99

P(Detected/Non-Spam) = P(false positives) = 0.05

Using Bayes Theorem, P(Non-Spam/Spam Detected) = ( P(Spam Detected/Non-Spam) x P(Non-Spam) ) / P(Spam Detected)

= 0.05*0.5 / 0.5*0.99

= 5/99