Sure, let's break this down step-by-step.
1. Total Number of Sections: The spinner has 13 sections, each labeled with a number from 1 to 13.
2. Even Numbers on the Spinner: The even numbers between 1 and 13 are 2, 4, 6, 8, 10, and 12. Therefore, there are:
[tex]\[
6 \text{ even numbers}
\][/tex]
3. Numbers Less than 5 on the Spinner: The numbers less than 5 are 1, 2, 3, and 4. Therefore, there are:
[tex]\[
4 \text{ numbers less than 5}
\][/tex]
4. Union of Even Numbers and Numbers Less than 5: We need to determine the unique numbers that fall into either category. The numbers we have listed are: 1, 2, 3, 4, 6, 8, 10, and 12. Note that 2 and 4 appear in both categories, but we count them only once.
Therefore, the total unique numbers that are either even or less than 5 are:
[tex]\[
8 \text{ unique numbers}
\][/tex]
5. Probability Calculation: The probability that the arrow lands on a section with an even number or a number less than 5 is given by the number of favorable outcomes divided by the total number of outcomes.
Thus, the probability is:
[tex]\[
\frac{\text{Number of favorable outcomes}}{\text{Total number of sections}} = \frac{8}{13}
\][/tex]
Given these calculations, the correct answer is:
C. [tex]\(\frac{8}{13}\)[/tex]
