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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 the table, the company that makes snack A calculates probabilities related to a randomly selected person.

\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}

Complete the conclusions based on the data in the table.

Given a person who has eaten snack A before, the customer will [tex]$\square$[/tex]

Given a person who has not eaten snack A before, the customer will want to eat snack [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
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.
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