To solve this problem, we need to calculate the probability $P(>8)$, which refers to the probability that the spinner lands on a number greater than 8. Let's break it down:

Step 1: Identify the total number of sections on the spinner.

The spinner has numbers from 1 to 12, which means there are 12 equally likely outcomes.

Step 2: Identify the favorable outcomes.

We are interested in outcomes where the number is greater than 8. The numbers greater than 8 on the spinner are 9, 10, 11, and 12. So there are 4 favorable outcomes.

Step 3: Calculate the probability.

The probability of landing on a number greater than 8 is given by the ratio of favorable outcomes to total outcomes:

$P(>8) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{12}$

Step 4: Simplify the fraction.

$\frac{4}{12} = \frac{1}{3}$

Thus, the probability $P(>8) = \frac{1}{3}$.

Would you like further details or explanations on this?

Here are 5 related questions to expand on this concept:

1. What is the probability of landing on a number less than 5?
2. What is the probability of landing on an odd number?
3. What is the probability of landing on a number between 6 and 10 (inclusive)?
4. How would the probability change if the spinner had 16 sections instead of 12?
5. What is the probability of landing on a number that is a multiple of 3?

Tip: Always reduce fractions when solving probability problems to give the simplest answer.