SOLUTION: To reduce laboratory costs, water samples from four public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sa
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Question 1160700: To reduce laboratory costs, water samples from four 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 0.008 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from four 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? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Probability that 4 samples will have at least 1 positive is 1-probabliity they have 0, which is 1-0.992^4=0.0316
I don't know what constitutes "low enough". It would happen about 1 in 33 times, so that would suggest it would be worth combining samples.
