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Each participant tastes snack A and snack B and then chooses their favorite. Some participants have eaten snack [tex][tex]$A$[/tex][/tex] 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|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}{c}
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 [tex][tex]$A$[/tex][/tex] before, the customer will [tex][tex]$\square$[/tex][/tex]
- Given a person who has not eaten snack [tex][tex]$A$[/tex][/tex] before, the customer will want to eat snack [tex][tex]$\square$[/tex][/tex]

Sagot :

GinnyAnswer
To fill in the blanks in the given conclusions based on the data in the table, let's proceed with the step-by-step reasoning:

1. Given a person who has eaten snack A before:
- According to the data, among those who have eaten snack A before, 144 out of 236 participants prefer snack A.
- This is a probability of approximately 0.610 (or 61.02%).
- Therefore, given a person who has eaten snack A before, it is most likely that the customer will prefer snack A.

2. Given a person who has not eaten snack A before:
- Among those who have not eaten snack A before, 228 out of 336 participants prefer snack B.
- This is a probability of approximately 0.679 (or 67.86%).
- Consequently, given a person who has not eaten snack A before, it is most likely that the customer will want to eat snack B.

So the completed conclusions will be:

- 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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