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Part A
Create a list of all the possible outcomes for three days of drink selections. Use the abbreviations W, M, T, and L to represent water, milk, tea, and lemonade.

Part B
Based on the list you created in part A, how many possible outcomes are there?

Part C
What is the probability that Erin drinks lemonade one day, tea one day, and water one day?

Part D
What is the probability that Erin drinks water two days and lemonade one day?

Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Let's tackle the problem step-by-step.

### Part A: List of all possible outcomes

The spinner has four sections: water (W), milk (M), tea (T), and lemonade (L). Erin spins the spinner three times, so we need to list all the possible outcomes for three days of drink selections. 

Each day has 4 possibilities, so the total number of combinations is \( 4^3 = 64 \).

The list of all possible outcomes (each combination of three spins) is:
```
WWW, WWM, WWT, WWL, WMW, WMM, WMT, WML, WTW, WTM, WTT, WTL, WLW, WLM, WLT, WLL,
MWW, MWM, MWT, MWL, MMW, MMM, MMT, MML, MTW, MTM, MTT, MTL, MLW, MLM, MLT, MLL,
TWW, TWM, TWT, TWL, TMW, TMM, TMT, TML, TTW, TTM, TTT, TTL, TLW, TLM, TLT, TLL,
LWW, LWM, LWT, LWL, LMW, LMM, LMT, LML, LTW, LTM, LTT, LTL, LLW, LLM, LLT, LLL
```

### Part B: Number of possible outcomes

As calculated, there are \( 4^3 = 64 \) possible outcomes.

### Part C: Probability that Erin drinks lemonade one day, tea one day, and water one day

To find this probability, we need to count how many of the outcomes contain exactly one L, one T, and one W, and then divide by the total number of outcomes.

First, let's count the favorable outcomes:
The combinations that include exactly one L, one T, and one W are:

```
LTW, LWT, TLW, TWL, WLT, WTL
```

There are 6 favorable outcomes.

Thus, the probability is:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{64} = \frac{3}{32} \]

### Part D: Probability that Erin drinks water two days and lemonade one day

We need to count how many outcomes have exactly two W's and one L:

The combinations that include exactly two W's and one L are:

```
WWL, WLW, LWW
```

There are 3 favorable outcomes.

Thus, the probability is:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{64} \]

### Self-Evaluation

1. Rate your work on a scale of 1 to 5.
2. Write a brief evaluation of your work below. Note what you learned and what challenged you.

I will assume you want to do this part on your own.

---

Do you have any questions or need further details?

Here are 5 questions you might ask next:
1. Can you explain how to determine the total number of possible outcomes in more detail?
2. How can we systematically count the favorable outcomes for such problems?
3. Can you show how to compute probabilities for other similar scenarios?
4. What are some common mistakes to avoid when calculating probabilities?
5. How can we apply these probability concepts to more complex problems?

**Tip:** When dealing with probability problems, always clearly define the sample space and carefully count the favorable outcomes.

Explore the calculation of probabilities for three days of drink selections by Erin, involving water, milk, tea, and lemonade. Understand how to determine the total number of outcomes, count favorable outcomes, and compute probabilities based on specific drink choices. Suitable for students in Grades 9-12.

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