To reduce laboratory costs, water samples from six public swimming pools are com

Question

To reduce laboratory costs, water samples from six public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.006 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from six public swimming areas will reveal the presence of bacteria. 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 quite low, indicating that further testing is necessary for all of the combined samples. B. The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event. C. The probability is quite low, indicating that further testing is not necessary for any of the combined samples. The probability is quite low, indicating that further testing of the individual samples will not be a rarely necessary event.

Explanation / Answer

It is given that from the past results, probability of finding bacteria in a public swimming area = p = 0.006

total number of swimming pools from where we take sample = n = 6

If at least one sample contain bacteria then the test is positive

So here we want to find P( X >= 1)

= 1 - P ( X = 0)

for binomial distribution P(X = 0) = (1 - p)^n = (1 - 0.006)^6 = 0.965

So that P( X >= 1) = 1 - 0.965 = 0.035

Since p = 0.035 < 0.05 so it is unusual and therefor we can say that it is low enough

So correct option is D

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