Sure, let's analyze the table and calculate the probabilities based on it.
First, we need to address the following questions:
1. What is the probability that a person who has eaten snack A before prefers snack A?
2. What is the probability that a person who has not eaten snack A before prefers snack B?
Let's go through them step-by-step.
Step 1: Calculating the probability that a person who has eaten snack A before prefers snack A:
We have:
- Number of participants who have eaten snack A before and prefer snack A = 144
- Number of participants who have eaten snack A before = 236
The probability [tex]\(\mathrm{P(prefer \, snack \, A \mid has \, eaten \, snack \, A \, before)}\)[/tex] is calculated as follows:
[tex]\[
\mathrm{P(prefer \, snack \, A \mid has \, eaten \, snack \, A \, before)} = \frac{144}{236} \approx 0.6101694915254238
\][/tex]
So, given a person who has eaten snack A before, the customer will most likely prefer snack A (with a probability of approximately 0.610).
Step 2: Calculating the probability that a person who has not eaten snack A before prefers snack B:
We have:
- Number of participants who have not eaten snack A before and prefer snack B = 228
- Number of participants who have not eaten snack A before = 336
The probability [tex]\(\mathrm{P(prefer \, snack \, B \mid has \, not \, eaten \, snack \, A \, before)}\)[/tex] is calculated as follows:
[tex]\[
\mathrm{P(prefer \, snack \, B \mid has \, not \, eaten \, snack \, A \, before)} = \frac{228}{336} \approx 0.6785714285714286
\][/tex]
So, given a person who has not eaten snack A before, the customer will most likely prefer snack B (with a probability of approximately 0.679).
Summary:
- 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.
