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

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**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**

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**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
**Question 1:** - **A** and **E** are the correct ways to simulate the number of games the football team will win. **Question 2:** - The shoreline changes by $$ -5 \frac{1}{4} $$ feet after 7 years.

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