Law of total probability Bayes formula Show steps System may

Law of total probability, Bayes formula.. Show steps

System may become infected by some spyware through the internet or e-mail. Seventy percent of the time the spyware arrives via the internet, thirty percent of the time via e-mail. If it enters via the internet, the system detects it immediately with probability 0.6. If via e-mail, it is detected with probability 0.8. What percentage of times is this spyware detected?

Solution

P(Arrives via internet) = 0.7

P(Arrives via email) = 0.3

Probability that it is detected

=Probability that it arrives via email*Probability that it is detected via email + Probability that it arrives via internet*Probability that it is detected via internet

=0.3*0.8+0.7*0.6

=0.24+0.42

=0.66