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 wil always test positive, 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 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? The probability is not low, so further testing will be necessary for all of the combined mixtures. The probability is not low, so further testing of the individual samples will be a rarely necessary event. The probability is not low, so further testing of the individual samples will not be a rarely necessary event The probability is not low, so further testing will not be necessary for any of the mixtures. ⓔ A. O B. O C. O D.

Answer 1

P(single sample testing positive) = 0.05

P(single sample testing negative) = 1 - 0.05 = 0.95

P(mixture of sample giving positive result) = 1 - P(all single samples in mixture giving negative result)

= 1 - 0.95³

= 0.143

A probability can be considered low enough to be rare if it is below 0.05

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