This is pure Bayes theorem and I knew that immediately, but I still fumbled the setup for a second because the base rate being so low felt counterintuitive.
Recognize this as a Bayesian probability problem and set up the calculation using the base rate, true positive rate, and false positive rate. Compute the probability of being fake given a flag by dividing the probability of a true positive by the total probability of a flag (true positives + false positives). Clearly explain each step and interpret the result in the context of the platform's detection system.
Pro tip: After computing the exact probability, mention that this illustrates the base rate fallacy and discuss the practical implications for the platform, such as the need for additional verification steps or adjusting the threshold to balance precision and recall.
Extract the base rate (2% fake), true positive rate (90% of fakes flagged), and false positive rate (5% of legitimate flagged).
Let F be the event that an account is fake, and A be the event that it is flagged. We need P(F|A).
Use the formula P(F|A) = P(A|F) * P(F) / [P(A|F)*P(F) + P(A|F^c)*P(F^c)].
Calculate numerator: 0.9 * 0.02 = 0.018. Denominator: 0.018 + 0.05 * 0.98 = 0.018 + 0.049 = 0.067. Then P(F|A) = 0.018 / 0.067 ≈ 0.2687 or 26.87%.
Explain that despite the high true positive rate, the low base rate means only about 27% of flagged accounts are actually fake, highlighting the base rate fallacy.
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