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### Problem Recap:
- There are 30 IB students.
- 20 study mathematics SL.
- 12 study physics.
- 8 study both mathematics SL and physics.

### Question:
Find the probability that a randomly selected student does **not** study both subjects.

### Solution:
1. **Total number of students:** \( N = 30 \)
2. **Number of students who study both subjects (Mathematics SL and Physics):** \( n(\text{Math} \cap \text{Physics}) = 8 \)
3. **Number of students who do not study both subjects:** 
   \[
   n(\text{not both}) = N - n(\text{Math} \cap \text{Physics}) = 30 - 8 = 22
   \]
4. **Probability that a randomly selected student does not study both subjects:** 
   \[
   P(\text{not both}) = \frac{n(\text{not both})}{N} = \frac{22}{30} = \frac{11}{15}
   \]

### Answer:
The correct option is **1) \(\frac{11}{15}\)**.

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Here are 5 related questions:
1. What is the probability that a randomly selected student studies both mathematics SL and physics?
2. How would the probability change if 5 more students were studying both subjects?
3. What is the probability that a student studies only one of the subjects?
4. How do you calculate the probability of a student studying at least one subject?
5. What would happen to the probability if the total number of students increased?

**Tip:** When calculating probabilities, make sure that the total outcomes and the desired outcomes are clearly identified to avoid confusion.

In a class of 30 IB students, 20 study mathematics SL, 12 study physics, and 8 study both of these subjects. Find the probability that a randomly selected student does not study both of these subjects.

Find out how to calculate the probability that a student does not study both mathematics SL and physics in a class of 30 IB students. This problem involves key concepts in probability and set theory, suitable for Grades 10-12.

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