APFIVE Applying The Law Of Total Probability
On a university campus, 60% of the computers run Windows, 30% run Apple, and 10% run Linux. A virus affects 3% of Windows, 2% of Apple, and 1% of Linux computers. All of the following statements are true except:
A
Each branch’s contribution (the product of the OS proportion and its virus rate) adds to form the overall infection probability.
B
The overall probability that a computer is not infected is given by $$1 - (0.6*0.03 + 0.3*0.02 + 0.1*0.01)$$.
C
Multiplying the probabilities along each branch of the tree is valid because the events are independent.
D
The overall probability a computer is infected is calculated as $$0.6*0.03+0.3*0.02+0.1*0.01$$, which equals 0.027.
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