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 three 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 0.1, find the probability of a positive result for three 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 be a rarely necessary event. O B. The probability is not low, so further testing of the individual samples will not be a rarely necessary event. Click to select your answer(s) Save for Later 247 PM 81 Type here to search up pg dn end g up 9 144 On ock

Explanation / Answer

P( The result of the test is positive for the three combined samples)

= P( at least one of the sample is positive)

= 1 - P( all are negative)

= 1 - (0.9 *0.9 * 0.9) = 1 - 0.729 = 0.271

Since this probability is not low we need to test each sample from the combined samples.

So correct choice is D

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