Problem of choosing over time

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I have a set of 100 diseased people. According to data, the probability of them getting themselves reported/tested is 0.03, which means that only 1 in every 30 cases will get reported. Let us assume that the count of the diseased remains a constant over 10 days. How should the probability of reporting/testing be interpreted? Should I expect that at the end of 10 days there should only be 3-4 cases or 30-35 (assuming that 3-4 get reported daily)?