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 0.005 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? the probability of a positive test result is.015 (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 not necessary for any of the combined samples. b. the probability is quite high, indicating that further testing of the individual samples will frequently be a necessary event. c. the probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event. d. the probability is quite high, indicating that further testing is necessary for all of the combined samples.

Explanation:

Step1: Identify probability concept

We use the addition rule for independent events.

Step2: Calculate combined probability

The probability of finding bacteria in one public - swimming area is $p = 0.005$. Since the samples are from three independent public - swimming areas, and we want to find the probability that at least one of them has bacteria. The probability that none of them has bacteria is $(1 - 0.005)^3$. Then the probability that at least one has bacteria is $P = 1-(1 - 0.005)^3$.
$P=1-(0.995)^3=1 - 0.985074875=0.014925125\approx0.015$.

Step3: Analyze the probability value

A probability of $0.015$ (or $1.5\%$) is relatively low. It means that further testing of the individual samples will be a rarely necessary event.

Answer:

C. The probability is quite low, indicating that further testing of the individual samples will be a rarely necessary event.