Total Probability Calculation
On a university campus, 60 percent of computers run Windows, 30 percent run an Apple OS, and 10 percent run Linux. The respective probabilities of a virus infection for these operating systems are 0.03, 0.02, and 0.01. A researcher calculated the overall probability of a computer being infected by summing these three probabilities (0.03 + 0.02 + 0.01 = 0.06). Which of the following best describes the error in the researcher’s process?
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 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 the multiplication of probabilities, which should have been added instead.
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