Sure, let's break this down step-by-step, based on the data provided:
1. The table presents data for people who have either eaten or not eaten snack A before and their preferences for snack A or snack B.
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Prefers Snack A & Prefers Snack B & Total \\
\hline
Has Eaten Snack A before & 144 & 92 & 236 \\
\hline
Has Not Eaten Snack A before & 108 & 228 & 336 \\
\hline
Total & 252 & 320 & 572 \\
\hline
\end{tabular}
\][/tex]
2. Calculate the probability that a person who has eaten snack A before prefers snack A:
- Number of people who have eaten snack A and prefer snack A: 144
- Total number of people who have eaten snack A: 236
Probability = [tex]\( \frac{144}{236} = 0.6101694915254238 \)[/tex]
3. Calculate the probability that a person who has not eaten snack A before prefers snack B:
- Number of people who have not eaten snack A and prefer snack B: 228
- Total number of people who have not eaten snack A: 336
Probability = [tex]\( \frac{228}{336} = 0.6785714285714286 \)[/tex]
Now, let's fill in the conclusions based on these probabilities:
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.
