Question

it is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails and the probability for a flase positive is 5%. What is the probability that an email is detected as spam

Answer 1

0.52 = 52% probability that an email is detected as spam.

Explanation:

Probability that an email is detected as spam:

99% of 50%(are spam).

5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).

What is the probability that an email is detected as spam?

`p = 0.99*0.5 + 0.05*0.5 = 0.52`

0.52 = 52% probability that an email is detected as spam.