Consider a set of nine separate water samples from a region where the prevalence of bacterial contamination is 30%. Assuming the binomial distribution is appropriate, what is the probability that exactly three of the samples indicate contamination?

Question

Quizplus · Accepted Answer

The probability of exactly three samples showing contamination out of nine, given a 30% contamination rate, can be calculated using the binomial probability formula: $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n=9$, $k=3$, and $p=0.30$. This calculation results in approximately 0.267.

Consider a Set of Nine Separate Water Samples from a Region