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Sagot :
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.
### 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.
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