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Each participant tastes snack A and snack [tex][tex]$B$[/tex][/tex] 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|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 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 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.
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