APFIVE On a university campus, 60% of the computers run Windows with a 3% infection rate, 30% run Apple with a 2% infection rate, and 10% run Linux with a 1% infection rate. A researcher computed the overall probability of a computer being infected by simply adding 0.03, 0.02, and 0.01 to get 0.06. Identify the mistake in the researcher’s process.
The error is ignoring the weights of each operating system; the correct probability is calculated using the law of total probability: 0.6×0.03 + 0.3×0.02 + 0.1×0.01 = 0.018 + 0.006 + 0.001 = 0.025.
The error is in assuming that the probabilities of being infected are independent across operating systems.
There is no mistake; the overall probability is indeed 0.06.
The error is in the multiplication of probabilities, which should have been added instead.
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