Final answer:
To calculate the probability of detecting 1 or more bacteria in the sample, we need to find the probability of not detecting any bacteria and subtract it from 1. We can use the Poisson distribution with an average concentration of 10 organisms/L.
Step-by-step explanation:
To calculate the probability of detecting 1 or more bacteria in the sample, we need to find the probability of not detecting any bacteria and subtract it from 1. The probability of not detecting any bacteria in the sample is equal to the probability that the concentration of bacteria in the sample is 0 organisms/L. The average concentration is 10 organisms/L, so the probability of detecting 1 or more bacteria is 1 minus the probability of having a concentration of 0 organisms/L.
To find the probability, we can use a Poisson distribution. The Poisson distribution is often used for counting events that occur randomly in a fixed interval of time or space. In this case, the average concentration of bacteria is lambda = 10 organisms/L. Using the Poisson formula:
P(X = k) = (lambda^k * e^(-lambda)) / k!
Where lambda is the average concentration and k is the number of occurrences (in this case, the number of bacteria).
The probability of having 0 bacteria in the sample is:
P(X = 0) = (10^0 * e^(-10)) / 0! = e^(-10) ≈ 0.000045, rounded to 6 decimal places.
Therefore, the probability of detecting 1 or more bacteria in the sample is:
1 - P(X = 0) = 1 - 0.000045 ≈ 0.999955, rounded to 6 decimal places.