To solve the given problem, we need to calculate the relative frequencies for three specific categories: students who have been to Alaska, students who have been to Hawaii but not Alaska, and students who have not been to either Alaska or Hawaii.
First, let's understand the total number of students surveyed by using the given two-way table. The total number of students is 50.
### 1. Relative frequency of students who have been to Alaska
The number of students who have visited Alaska is given in the table:
- Students who have visited Alaska (whether or not they visited Hawaii): 14
To find the relative frequency, we use the formula:
[tex]\[ \text{Relative frequency} = \frac{\text{Number of students who have been to Alaska}}{\text{Total number of students}} \][/tex]
Substituting the values:
[tex]\[ \text{Relative frequency of students who have been to Alaska} = \frac{14}{50} = 0.28 \][/tex]
### 2. Relative frequency of students who have been to Hawaii but not Alaska
The number of students who have been to Hawaii but not Alaska is given as 15.
To find the relative frequency, we use the formula:
[tex]\[ \text{Relative frequency} = \frac{\text{Number of students who have been to Hawaii but not Alaska}}{\text{Total number of students}} \][/tex]
Substituting the values:
[tex]\[ \text{Relative frequency of students who have been to Hawaii but not Alaska} = \frac{15}{50} = 0.3 \][/tex]
### 3. Relative frequency of students who have not been to Alaska or Hawaii
The number of students who have not been to either Alaska or Hawaii is given as 21.
To find the relative frequency, we use the formula:
[tex]\[ \text{Relative frequency} = \frac{\text{Number of students who have not been to Alaska or Hawaii}}{\text{Total number of students}} \][/tex]
Substituting the values:
[tex]\[ \text{Relative frequency of students who have not been to Alaska or Hawaii} = \frac{21}{50} = 0.42 \][/tex]
### Summary
- The relative frequency for students who have been to Alaska is [tex]\(0.28\)[/tex].
- The relative frequency for students who have been to Hawaii but not Alaska is [tex]\(0.3\)[/tex].
- The relative frequency for students who have not been to Alaska or Hawaii is [tex]\(0.42\)[/tex].
