Question

To reduce laboratory​ costs, water samples from three 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 .01 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from three 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 1

The probability of finding bacteria in a combined sample from three public swimming areas is 0.0297. Further testing of the individual samples is rarely necessary.

Step-by-step explanation:

The probability of finding bacteria in a single public swimming area is 0.01, according to past results. To find the probability that a combined sample from three public swimming areas will reveal the presence of bacteria, we can use the complement rule for probabilities. The probability of not finding bacteria in a single area is 1 - 0.01 = 0.99. Since the three samples are combined, the probability of not finding bacteria in any of the three areas is 0.99^3 = 0.9703.

To find the probability of finding bacteria in at least one of the three areas, we can subtract the probability of not finding bacteria in any of the three areas from 1. So, the probability of finding bacteria in the combined sample is 1 - 0.9703 = 0.0297.

The probability of finding bacteria in the combined sample is relatively low, so further testing of the individual samples is rarely necessary.