Question

the two - way table shows the preferred vacation destination for people in different age groups.
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: Calculate probability for each option

• Option 1: Probability that a randomly - selected adult chose Hawaii.

The number of adults who chose Hawaii is \(64\), and the number of adults is \(129\). The probability is \(\frac{64}{129}
eq\frac{147}{355}\) (since \(\frac{147}{355}\) is the probability of choosing Hawaii out of all people).

• Option 2: Probability that a randomly - selected person who chose Hawaii is a teenager.

The number of teenagers who chose Hawaii is \(50\), and the number of people who chose Hawaii is \(147\). The probability is \(\frac{50}{147}
eq\frac{33}{50}\) (where \(33\) is the number of children who chose Hawaii).

• Option 3: Probability that a randomly - selected child chose Florida.

The number of children who chose Florida is \(62\), and the number of children is \(109\). The probability is \(\frac{62}{109}
eq\frac{62}{95}\) (where \(95\) is the total number of people who chose Florida).

• Option 4: Probability that a randomly - selected person who chose Mexico is a child.

The number of children who chose Mexico is \(14\), and the number of people who chose Mexico is \(113\). The probability is \(\frac{14}{113}\).

Answer:

The probability that a randomly selected person who chose Mexico as the preferred destination is a child is \(\frac{14}{113}\) (Option 4).