Using Composite Water Samples The Orange CountyDepartment of Public Health tests

Question

Using Composite Water Samples The Orange CountyDepartment of Public Health

tests water for contamination due to the presence of £coli (Escherichia coli) bacte-

ria. To reduce laboratory costs, water samples from six publicswimming areas are

combined for one test, and further testing is done only if thecombined sample fails

Based on past results, there is a 2% chance of finding E.coli bacteria in a public

swimming area. Find the probability that a combined sample fromsix public swim-

ming areas will reveal the presence of E. colibacteria.

Explanation / Answer

6 samples from public swimming areas. Each sample has aprobability of 2% containing Ecoli. Question: what is the probability of the combined samplehaving Ecoli? P(combined sample has E coli) = 1- P(non of the 6 samples hasEcoli) = 1-(1-0.02)6 = 0.114

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