Select the correct answer from each drop-down menu.

Each participant tastes snack [tex][tex]$A$[/tex][/tex] 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 randomly selected person.

\begin{tabular}{|c|l|l|l|}
\hline & Prefers Snack A & Prefers Snack B & Total \\
\hline \begin{tabular}{c}
Has Eaten Snack \\
A before
\end{tabular} & 144 & 92 & 236 \\
\hline \begin{tabular}{l}
Has Not Eaten \\
Snack A before
\end{tabular} & 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 probability that the customer will prefer snack B is [tex][tex]$\square$[/tex][/tex].

Given a person who has not eaten snack A before, the probability that the customer will prefer snack A is [tex][tex]$\square$[/tex][/tex].



Answer :

Sure, let's analyze the data step-by-step and draw the necessary conclusions.

1. Given a person who has eaten snack A before, the probability that they prefer snack B:
- The number of people who have eaten snack A before and prefer snack B is [tex]\( 92 \)[/tex].
- The total number of people who have eaten snack A before is [tex]\( 236 \)[/tex].
- The probability is calculated as:
[tex]\[ \text{Probability} = \frac{92}{236} \approx 0.38983 \][/tex]
- Converting this probability to a percentage:
[tex]\[ 0.38983 \times 100 \approx 38.98\% \][/tex]
- Thus, "Given a person who has eaten snack A before, the customer will change to snack B 38.98% of the time.

2.
Given a person who has not eaten snack A before, the probability that they prefer snack A:
- The number of people who have not eaten snack A before and prefer snack A is [tex]\( 108 \)[/tex].
- The total number of people who have not eaten snack A before is [tex]\( 336 \)[/tex].
- The probability is calculated as:
[tex]\[ \text{Probability} = \frac{108}{336} \approx 0.32143 \][/tex]
- Converting this probability to a percentage:
[tex]\[ 0.32143 \times 100 \approx 32.14\% \][/tex]
- Thus, "Given a person who has not eaten snack A before, the customer will want to eat snack A" 32.14% of the time.

Based on the above calculations, we complete the conclusions as follows:

Complete the conclusions based on the data in the table.
1. Given a person who has eaten snack A before, the customer will change to snack B 38.98%.
2. Given a person who has not eaten snack A before, the customer will want to eat snack A.