Directions: Find or select the best answer. Record your response on your answer sheet. 1. Henrietta heard that the school's football team has a \( 1 / 3 \) probability of winning each of their next 5 games. Select all the ways Henrietta could accurately simulate the number of games the football team will win. A. Roll a standard number cube 5 times. Count the number of 1 's and 2 's. B. Put the numbers 1 through 5 in a bag. Pick a number from the bag C. Roll a standard number cube 5 times. Count the number of ones D. Mark a spinner with 3 equally-sized sections. Write "win" on 2 of the sections. Spin the spinner 5 times and count the number of times it lands on "win." E. Put 2 white chips and 1 red chip in a bag. Draw a chip from the bag, record its result, and put it back in the bag. Do this 5 times and count the number of red chips drawn. 2. The amount of shore at a local beach changes an average of \( -3 / 4 \) foot each year. What is the change in the amount of shore after 7 years? A. \( 5 \frac{1}{4} \) feet B. \( \frac{3}{20} \) foot C. \( -\frac{3}{20} \) foot D. \( -5 \frac{1}{4} \) feet

**Question 1:** Henrietta wants to simulate the number of games the football team will win, where each game has a \( \frac{1}{3} \) probability of being a win. Let's evaluate each option: - **A.** *Roll a standard number cube 5 times. Count the number of 1's and 2's.* - A standard die has numbers 1-6. Counting the number of 1's and 2's gives a probability of \( \frac{2}{6} = \frac{1}{3} \) for each trial. - **This accurately simulates the probability.** - **B.** *Put the numbers 1 through 5 in a bag. Pick a number from the bag.* - Each number has a probability of \( \frac{1}{5} \), which is not equal to \( \frac{1}{3} \). - **This does not accurately simulate the probability.** - **C.** *Roll a standard number cube 5 times. Count the number of ones.* - Counting only the number of 1's gives a probability of \( \frac{1}{6} \) for each trial. - **This does not accurately simulate the probability.** - **D.** *Mark a spinner with 3 equally-sized sections. Write "win" on 2 of the sections. Spin the spinner 5 times and count the number of times it lands on "win."* - "Win" has a probability of \( \frac{2}{3} \), which is not equal to \( \frac{1}{3} \). - **This does not accurately simulate the probability.** - **E.** *Put 2 white chips and 1 red chip in a bag. Draw a chip from the bag, record its result, and put it back in the bag. Do this 5 times and count the number of red chips drawn.* - Drawing a red chip has a probability of \( \frac{1}{3} \) for each trial. - **This accurately simulates the probability.** **Correct Answers for Question 1:** **A** and **E** --- **Question 2:** The shoreline changes by an average of \( -\frac{3}{4} \) foot each year. To find the change over 7 years: \[ \text{Total Change} = \left( -\frac{3}{4} \right) \times 7 = -\frac{21}{4} = -5 \frac{1}{4} \text{ feet} \] **Correct Answer for Question 2:** **D.** \( -5 \frac{1}{4} \) feet