\begin{tabular}{l} Permutations and Probability \\ Determine the following probabilities. Enter your answers as percents rounded to four decimal \\ places. \\ The student council has 9 members where 5 of the members are Seniors. They need to choose a \\ President, Vice President, Secretary and Treasurer. \\ If the members are randomly assigned to the positions, what is the probability that the President is a \\ Senior? \\ \( \begin{array}{l}55.56 \\ \begin{array}{l}\text { Jacy has } 13 \text { books and he wants to read } 4 \text { over the summer. He has } 9 \text { fiction books and } 4 \text { nonfiction } \\ \text { books. } \\ \text { If Jacy randomly selects the } 4 \text { books, what is the probability that the first } 3 \text { books are fiction and the } \\ \text { next } 1 \text { books are nonfiction? } \\ \text { \% }\end{array}\end{array} \begin{array}{l}\text { \% }\end{array} \) \\ \hline\end{tabular}

Let's solve the two probability problems you've presented. --- ### **1. Probability that the President is a Senior** **Given:** - Total members = 9 - Seniors = 5 - Positions to be filled = President, Vice President, Secretary, Treasurer **Question:** What is the probability that the President is a Senior? **Solution:** The probability that the President is a Senior is simply the ratio of the number of Seniors to the total number of members. \[ \text{Probability} = \frac{\text{Number of Seniors}}{\text{Total Members}} = \frac{5}{9} \approx 0.5555555556 \] **Converted to Percentage:** \[ 0.5555555556 \times 100 \approx 55.5556\% \] **Answer:** **55.5556%** --- ### **2. Probability that Jacy Selects 3 Fiction Books Followed by 1 Nonfiction Book** **Given:** - Total books = 13 - Fiction books = 9 - Nonfiction books = 4 - Books to be read = 4 - Selection order: First 3 books are fiction, and the 4th book is nonfiction. **Question:** What is the probability that the first 3 books selected are fiction and the 4th book is nonfiction? **Solution:** Since the selection is without replacement and order matters, we'll calculate the probability step by step. 1. **First Book is Fiction:** \[ \frac{9}{13} \] 2. **Second Book is Fiction:** \[ \frac{8}{12} = \frac{2}{3} \] 3. **Third Book is Fiction:** \[ \frac{7}{11} \] 4. **Fourth Book is Nonfiction:** \[ \frac{4}{10} = \frac{2}{5} \] **Multiplying these probabilities together:** \[ \frac{9}{13} \times \frac{8}{12} \times \frac{7}{11} \times \frac{4}{10} = \frac{9 \times 8 \times 7 \times 4}{13 \times 12 \times 11 \times 10} = \frac{2016}{17160} \approx 0.1175824176 \] **Converted to Percentage:** \[ 0.1175824176 \times 100 \approx 11.7582\% \] **Answer:** **11.7582%** --- These calculations provide the required probabilities rounded to four decimal places as percentages.