Final answer:
To calculate the probability that one cubic meter of discharge contains at least 5 organisms in a Poisson process with 10 organisms per cubic meter, we use a complementary probability approach with the Poisson distribution formula.
Step-by-step explanation:
The question asks for the probability that one cubic meter of discharge contains at least 5 organisms when organisms are present in ballast water discharged from a ship according to a Poisson process with a concentration of 10 organisms per cubic meter (org/m3). To find this, we apply the Poisson distribution formula:
P(X ≥ k) = 1 - ∑i=0k-1 (e-λ λi / i!)
Where:
λ (lambda) is the mean number of occurrences in a given interval (in our case, λ=10 org/m3),
i is the number of occurrences (≥ 5 in our case),
e is the base of the natural logarithm (≈ 2.71828).
To calculate the probability of at least 5 organisms, we need the sum of the probabilities of having 0, 1, 2, 3, and 4 organisms and subtract that sum from 1. This complementary probability approach gives us the chance of having 5 or more organisms. We can compute this using a scientific calculator or statistical software that supports the Poisson distribution.