Using Composite Water Samples The Orange County Department o

Using Composite Water Samples The Orange County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia coif) bacteria. To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined 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 from six public swimming areas will reveal the presence of E. coli bacteria.

Solution

Probability of finding E. Coli. bacteria in a single swimming area = 2% or 0.02

Probability of not finding E. coli bacteria in any of the six selected swimming areas = (1-0.02)⁶ =0.886

Probability of finding E. coli bacteria in any of the six selected swimming area = 1-0.886 = 0.114