試題詳解

201. A group of 100 patients is tested, one patient at a time, for three risk factors for a certain disease until either all patients have been tested or a patient tests positive for more than one of these three risk factors. For each risk factor, a patient tests positive with probability p, where 0 ＜ p ＜ 1. The outcomes of the tests across all patients and all risk factors are mutually independent. Determine an expression for the probability that exactly n patients are tested, where n is a positive integer less than 100.
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