Let's analyze the given data step-by-step.
1. Given Data:
- The table shows the preferences of participants for snacks A and B, categorized by whether they have eaten snack A before or not.
2. Formulating Probabilities:
- The first part of the question asks about the preference given that a person has eaten snack A before. This translates to the probability of preferring snack A if the person has eaten snack A before.
- The second part of the question asks about the preference given that a person has not eaten snack A before. This translates to the probability of preferring snack B if the person has not eaten snack A before.
3. Extracting Relevant Data:
- For those who have eaten snack A before:
- Prefers A: 144
- Prefers B: 92
- Total: 236
- For those who have not eaten snack A before:
- Prefers A: 108
- Prefers B: 228
- Total: 336
4. Calculating Probabilities:
- Probability that a person who has eaten snack A before prefers snack A:
[tex]\[ \text{Probability} = \frac{\text{Number who prefer A}}{\text{Total who have eaten A before}} \][/tex]
[tex]\[
\frac{144}{236} \approx 0.610
\][/tex]
This means given a person who has eaten snack A before, there is approximately a 61.0% chance they will prefer snack A.
- Probability that a person who has not eaten snack A before prefers snack B:
[tex]\[ \text{Probability} = \frac{\text{Number who prefer B}}{\text{Total who have not eaten A before}} \][/tex]
[tex]\[
\frac{228}{336} \approx 0.679
\][/tex]
This means given a person who has not eaten snack A before, there is approximately a 67.9% chance they will prefer snack B.
Based on this data, we can fill in the blanks:
Given a person who has eaten snack A before, the customer will prefer snack A.
Given a person who has not eaten snack A before, the customer will want to eat snack B.
