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

Question

Testing for a disease can be made more efficient by combining samples. If the samples from four people are combined and the mixture tests negative, then all four samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assumin the probability of a single sample testing positive is 0.1, 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 rarely necessary? The probability of a positive test result is (Round to three decimal places as needed.) Is the probability low enough so that further testing of the individual samples is rarely necessary? A. The probability is not low, so further testing of the individual samples will not be a rarely necessary event. O B. The probability is not low, so further testing will be necessary for all of the combined mixtures ° C. The probability is not low, so further testing will not be necessary for any of the mixtures.

Explanation / Answer

When combining 4 samples, we must compute the probability
that at least one of the samples tests positive.

P(positive) = 0.1

P(negative) = 1 - 0.1 = 0.9

The opposite of "at least one positive" is "no positive".

the probability of no positive is:(0.9)^4 = 0.6561
therefore P(at least one is positive) = 1 - 06561 = 0.3439

The probability of a positive result is 0.3439

Therefore,

The probability is not low, so further testing of the individual samples will not be a rarely necessary event.

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