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A system may become infected by some spyware through the internet or email. Sixty percent of the time the spyware arrives via the internet, forty percent of the time via email. If it enters via the internet, the system detects it immediately with probability of 0.8. If via email, it is detected with probability 0.6. What percentage of times is this spyware detected?

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Answer:

This spyware is detected 72% of the time.

Step-by-step explanation:

We have these following probabilities:

A 60% probability that a spyware arrives via internet.

A 40% probability that a spyware arrives via email.

If it arrives via internet, an 80% probability that it is detected.

If it arrives via email, a 60% probability that it is detected.

What percentage of times is this spyware detected?

This is 80% or 60% and 60% of 40%. So

[tex]P = 0.8*0.6 + 0.6*0.4 = 0.72[/tex]

This spyware is detected 72% of the time.

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