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The problem in the image asks for the theoretical probability that the spinner, which has three equally sized sections (Blue, Pink, Gold), will land on the blue section on the next spin. Here's a breakdown of the problem:

- The spinner was spun 30 times, and it landed on the blue section 12 times. This information describes experimental probability, but the question specifically asks for **theoretical probability**.
  
The theoretical probability is based on the fact that the spinner has three equal sections, and thus the chance of landing on any section (Blue, Pink, or Gold) is equal.

### Step-by-Step Solution:
1. Since the spinner has 3 equal sections, the probability of landing on the blue section on any given spin is:
   \[
   P(\text{Blue}) = \frac{1}{3}
   \]
2. This is the theoretical probability because it’s based purely on the structure of the spinner (equal sections).

Thus, the **theoretical probability** that the spinner will land on the blue section on the next spin is \( \frac{1}{3} \).

Do you have any further questions, or would you like more details?

Here are 5 related questions:
1. What would be the experimental probability based on the data provided?
2. How does theoretical probability differ from experimental probability?
3. If the spinner landed on blue 15 times out of 30 spins, how would the experimental probability change?
4. How could you use a larger sample size to get closer to the theoretical probability?
5. How do probabilities change if the sections of the spinner are unequal in size?

**Tip**: Theoretical probability is always based on possible outcomes, while experimental probability is based on actual outcomes from trials.

What is the theoretical probability that the arrow will land on the blue section on the next spin, given that the spinner has three equal sections?

Learn how to calculate the theoretical probability of a spinner landing on the blue section. This problem explains the key concepts of theoretical probability, using a spinner with three equal sections. Suitable for students in Grades 6-8.

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