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Testing for a disease can be made more efficient by combining samples. If the samples from people are combined and the mixture tests​ negative, then all three samples are negative. On the other​ hand, one positive sample will always test​ positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 5%​, find the probability of a positive result for all three samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

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