Question

the two - way table shows the preferred vacation destination for people in different age groups.| | hawaii | mexico | florida | total || --- | --- | --- | --- | --- || child (less than 13 years old) | 33 | 14 | 62 | 109 || teenager (13 to 17 years old) | 50 | 42 | 25 | 117 || adult (18 years old and up) | 64 | 57 | 8 | 129 || total | 147 | 113 | 95 | 355 |which statement is true?- the probability that a randomly selected adult chose hawaii as the preferred destination is $\frac{147}{355}$.- the probability that a randomly selected person who chose hawaii as the preferred destination is a teenager is $\frac{33}{50}$.- the probability that a randomly selected child chose florida as the preferred destination is $\frac{62}{95}$.- the probability that a randomly selected person who chose mexico as the preferred destination is a child is $\frac{14}{113}$.

Explanation:

Step1: Analyze each option

• Option 1: Probability a random adult chose Hawaii. Number of adults: 129, Adults who chose Hawaii: 64. So probability should be $\frac{64}{129}$, not $\frac{147}{355}$. Eliminate.
• Option 2: Probability a person who chose Hawaii is a teenager. Number who chose Hawaii: 147, Teenagers who chose Hawaii: 50. Probability should be $\frac{50}{147}$, not $\frac{33}{50}$. Eliminate.
• Option 3: Probability a random child chose Florida. Number of children: 109, Children who chose Florida: 62. Probability should be $\frac{62}{109}$, not $\frac{62}{95}$. Eliminate.
• Option 4: Probability a person who chose Mexico is a child. Number who chose Mexico: 113, Children who chose Mexico: 14. Probability is $\frac{14}{113}$. This is correct.

Answer:

The probability that a randomly selected person who chose Mexico as the preferred destination is a child is $\frac{14}{113}$ (the last option: "The probability that a randomly selected person who chose Mexico as the preferred destination is a child is $\frac{14}{113}$").