Select the correct answer from each drop-down menu.

Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack A before and some have not. The results of the test are shown in a table. Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

**Prefers Snack APrefers Snack BTotalHas Eaten Snack A before**

144

92

236

**Has Not Eaten Snack A before**

108

228

336

**Total**

252

320

572

Complete the conclusions based on the data in the table.

Given a person who has eaten snack A before, the customer will stay with snack Achange to snack B.

Given a person who has not eaten snack A before, the customer will want to eat snack AB.

Let's interpret the table and calculate the relevant probabilities based on the given data.

|                | Prefers Snack A | Prefers Snack B | Total |
|----------------|-----------------|----------------|-------|
| **Has Eaten Snack A before**  | 144             | 92             | 236   |
| **Has Not Eaten Snack A before** | 108             | 228            | 336   |
| **Total**        | 252             | 320            | 572   |

### 1. **Given a person who has eaten snack A before**:
We want to determine the likelihood that they **stay with Snack A** or **change to Snack B**.

- The total number of people who have eaten Snack A before is **236**.
- Out of those, **144** prefer Snack A (i.e., they stay with Snack A).
- The probability of staying with Snack A = \( \frac{144}{236} \).

Since this probability is greater than 50%, the person is more likely to **stay with Snack A**.

### 2. **Given a person who has not eaten snack A before**:
We want to find out if they prefer Snack A or Snack B.

- The total number of people who have not eaten Snack A before is **336**.
- Out of those, **108** prefer Snack A, while **228** prefer Snack B.
- The probability of preferring Snack B = \( \frac{228}{336} \).

Since this probability is greater than 50%, the person is more likely to prefer **Snack B**.

### Conclusions:

1. **Given a person who has eaten Snack A before**, the customer will **stay with Snack A**.
2. **Given a person who has not eaten Snack A before**, the customer will want to eat **Snack B**.

Let me know if you want any further details or calculations!

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Here are 5 related questions:

1. What is the overall probability that a randomly selected person prefers Snack A?
2. How would the probabilities change if more people who hadn't eaten Snack A started preferring it?
3. What is the probability that a randomly selected person has not eaten Snack A before?
4. How can you calculate the likelihood of preferring Snack B overall, without conditions?
5. Can we predict future snack preferences based on this data?

**Tip**: When calculating conditional probabilities, always focus on the specific group in question, rather than the total population.

Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack A before and some have not. The results of the test are shown in a table. Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

Learn how to calculate conditional probabilities based on snack preferences. This example explains how to determine whether a person is likely to prefer Snack A or Snack B, using data interpretation and probability formulas. Suitable for high school students (Grades 9-12).

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