\begin{tabular}{|c|c|c|c|c|}
\hline & Hawaii & Mexico & Florida & Total \\
\hline \begin{tabular}{c}
Child \\
(Less Than 13 Years Old)
\end{tabular} & 33 & 14 & 62 & 109 \\
\hline \begin{tabular}{c}
Teenager \\
(13 to 17 Years Old)
\end{tabular} & 50 & 42 & 25 & 117 \\
\hline \begin{tabular}{c}
Adult \\
(18 Years Old and Up)
\end{tabular} & 64 & 57 & 8 & 129 \\
\hline Total & 147 & 113 & 95 & 355 \\
\hline
\end{tabular}

Which statement is true?

A. The probability that a randomly selected adult chose Hawaii as the preferred destination is [tex]$\frac{147}{355}$[/tex].

B. The probability that a randomly selected person who chose Hawaii as the preferred destination is a teenager is [tex]$\frac{33}{50}$[/tex].

C. The probability that a randomly selected child chose Florida as the preferred destination is [tex]$\frac{62}{95}$[/tex].

D. The probability that a randomly selected person who chose Mexico as the preferred destination is a child is [tex]$\frac{14}{113}$[/tex].



Answer :

Let's evaluate each statement given the probabilities derived from the data in the table.

### 1. The probability that a randomly selected adult chose Hawaii as the preferred destination:
To find this probability, we need to divide the number of adults who chose Hawaii by the total number of survey participants.

[tex]\[ \text{Probability} = \frac{\text{Number of adults who chose Hawaii}}{\text{Total number of people}} = \frac{64}{355} \approx 0.180 \][/tex]

This statement is false since it states [tex]\(\frac{147}{355}\)[/tex], which is not correct.

### 2. The probability that a randomly selected person who chose Hawaii as the preferred destination is a teenager:
To find this probability, we need to divide the number of teenagers who chose Hawaii by the total number of people who chose Hawaii.

[tex]\[ \text{Probability} = \frac{\text{Number of teenagers who chose Hawaii}}{\text{Total number of people who chose Hawaii}} = \frac{50}{147} \approx 0.340 \][/tex]

This statement is false since it states [tex]\(\frac{33}{50}\)[/tex], which is not correct.

### 3. The probability that a randomly selected child chose Florida as the preferred destination:
To find this probability, we need to divide the number of children who chose Florida by the total number of people who chose Florida.

[tex]\[ \text{Probability} = \frac{\text{Number of children who chose Florida}}{\text{Total number of people who chose Florida}} = \frac{62}{95} \approx 0.653 \][/tex]

This statement is true.

### 4. The probability that a randomly selected person who chose Mexico as the preferred destination is a child:
To find this probability, we need to divide the number of children who chose Mexico by the total number of people who chose Mexico.

[tex]\[ \text{Probability} = \frac{\text{Number of children who chose Mexico}}{\text{Total number of people who chose Mexico}} = \frac{14}{113} \approx 0.124 \][/tex]

This statement is true.

### Summary:
Only the statements "The probability that a randomly selected child chose Florida as the preferred destination is [tex]\(\frac{62}{95}\)[/tex]." and "The probability that a randomly selected person who chose Mexico as the preferred destination is a child is [tex]\(\frac{14}{113}\)[/tex]." are correct.