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

Testing for a disease can be made more efficient by combining samples. If the samples from five people are combined and the mixture testsnegative, then allfive 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 five samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarelynecessary?

The probability of a positive test result is ?

(Round to three decimal places asneeded.

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