1. The problem asks to solve a probability problem using one of the distributions: hypergeometric, binomial, or Poisson. 2. First, identify the type of problem: - Use the **hypergeometric distribution** when sampling without replacement from a finite population. - Use the **binomial distribution** when sampling with replacement or independent trials with two outcomes. - Use the **Poisson distribution** for modeling the number of events in a fixed interval when events occur independently and the average rate is known. 3. Since the problem statement is general, let's define the formulas: - Hypergeometric probability: $$P(X=k) = \frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}$$ where $N$ is population size, $K$ is number of successes in population, $n$ is sample size, and $k$ is number of observed successes. - Binomial probability: $$P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$$ where $n$ is number of trials, $p$ is probability of success, and $k$ is number of successes. - Poisson probability: $$P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$$ where $\lambda$ is the average rate and $k$ is number of events. 4. To solve a specific problem, plug in the known values into the appropriate formula and compute. Since no specific values or problem details were given, this is the general approach to solve problems using these distributions.