Question

Given a 0.005 probability of finding bacteria in one swimming pool area, what's the probability that the combined sample from 6 swimming pool areas will reveal the presence of bacteria? Is it low enough to skip further testing?

A) Probability of bacteria presence: 0.03; Further testing needed
B) Probability of bacteria presence: 0.03; Further testing not needed
C) Probability of bacteria presence: 0.03; Further testing depends on other factors
D) Probability of bacteria presence: 0.3; Further testing needed

Answer 1

The probability of finding bacteria in at least one of the six swimming pool areas is approximately 2.96%. This is calculated by finding the complement of the probability of not finding bacteria in any of the areas. Whether to conduct further testing depends on established safety protocols and acceptable risk levels.

Step-by-step explanation:

To calculate the probability of finding bacteria in at least one of the six swimming pool areas, we need to consider that the events of finding bacteria in each area are independent. The probability of not finding bacteria in one area is 1 - 0.005 = 0.995. The probability of not finding bacteria in all six areas is 0.995^6.

Now, the probability of finding bacteria in at least one area is the complement of not finding it in any, which is 1 - 0.995^6. Calculating this, 1 - 0.995^6 ≈ 0.0296 or 2.96%. This probability can be considered low, but the decision to skip further testing should depend on established safety protocols and acceptable risk levels.

Therefore, the correct answer is C) Probability of bacteria presence: 0.03; Further testing depends on other factors.