Question: Testing for a disease can be made more efficient by combining samples. If the samples from four people are combined and the mixture testsnegative, then

Testing for a disease can be made more efficient by combining samples. If the samples from

four people are combined and the mixture testsnegative, then

allfour samples are negative. On the otherhand, one positive sample will always testpositive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.05

find the probability of a positive result for four

samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarelynecessary?

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