https://file.aiquickdraw.com/mathbot/file/1725793697015lc68sigg.jpg

The problem is asking to determine the probability that someone chooses **a different type of toast on each day**, given the options and decisions shown in the diagram. Let's break it down step by step.

From the diagram, we have the following toast choices for **Day 1** and **Day 2**:

- Two toast options: **White** and **Brown**.
  
The tree diagram has been constructed to show each possibility:
1. Day 1: White, Day 2: White.
2. Day 1: White, Day 2: Brown.
3. Day 1: Brown, Day 2: White.
4. Day 1: Brown, Day 2: Brown.

We are tasked with calculating the probability that the person chooses a **different** type of toast each day. This means we need to focus on the cases where the choices are not the same on both days.

### Step 1: Identify the Favorable Outcomes
The favorable outcomes, where the toast choices differ, are:
- Day 1: White, Day 2: Brown.
- Day 1: Brown, Day 2: White.

These are two favorable outcomes.

### Step 2: Total Possible Outcomes
There are 4 total possible outcomes (as shown in the tree diagram):
1. White, White.
2. White, Brown.
3. Brown, White.
4. Brown, Brown.

### Step 3: Calculate the Probability
The probability of choosing different types of toast on each day is the ratio of favorable outcomes to the total possible outcomes:
\[
\text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{2}{4} = \frac{1}{2}
\]

### Final Answer:
The probability that the person chooses a different type of toast on each day is **\(\frac{1}{2}\)**.

Let me know if you'd like more details or have any other questions!

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Here are 5 related questions you could explore:
1. What is the probability of choosing the **same** type of toast on both days?
2. If there was a third day, how would the probability change for different toast choices each day?
3. How would the probability be affected if more types of toast were added to the selection?
4. What is the probability of choosing **white toast** on at least one of the days?
5. How can tree diagrams help in solving more complex probability problems?

**Tip**: When calculating probabilities using tree diagrams, make sure to count the total number of outcomes carefully to avoid errors in calculation!

One day, she chooses a type of toast at random and repeats this at the end of the next day. The tree diagram shows all the possible outcomes. Work out the probability that she chooses a different type of toast on each day. Give your answer as a fraction in its simplest form.

Learn how to calculate the probability of choosing a different type of toast on each day using a tree diagram. This problem is suitable for students in Grades 6-8 and involves key concepts such as probability and tree diagrams.

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