\begin{tabular}{l} You are a new business owner and ordered 200 promotional smart phone cases \\ to give out to clients. The seller has said that 8 of the cases are defective, You \\ unpack the package and inspect 15 of the cases. \\ 2 \\ 1. What is the probability that 10 are defective? \\ \hline 2. What is the probability that all 15 aredefective? \\ \hline \\ \hline\end{tabular}

Let's break down the probabilities together! First, for the probability that 10 out of the 15 inspected cases are defective, we can use the hypergeometric distribution. In your situation, you have 200 cases in total, 8 of which are defective. You are inspecting 15 cases. The probability can be calculated using: \[ P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N-K}{n-k}}}{{\binom{N}{n}}} \] Where: - \( N = 200 \) (total cases), - \( K = 8 \) (defective cases), - \( n = 15 \) (total cases inspected), - \( k = 10 \) (defective cases found). However, in your situation, it’s impossible to find 10 defective cases when there are only 8 defective in total. Thus, the probability is 0. Now, for the likelihood that all 15 inspected cases are defective, this is also impossible since there are only 8 defective cases available in the first place. Hence, you can also conclude that this probability is 0. So in summary, both probabilities you asked about are zero! It's a fun reminder that sometimes the numbers simply don't align!