10. 40 students enroll in a painting and crafts course, discriminated in the following way: 

P 15 (medium 7) 18 A

One is chosen at random from the group of students. Indicate the probability that the chosen student: 
• He is enrolled only in crafts.

To determine the probability that a randomly chosen student is enrolled only in crafts, we need to analyze the given dataTo determine the probability that a randomly chosen student is enrolled only in crafts, we need to analyze the given 

- \( P \): Total number of students in painting = 15
- \( P \cap A \): Number of students enrolled in both painting and crafts = 7
- \( A \): Total number of students in crafts = 18
- Total number of students = 40

First, let's calculate the number of students enrolled only in crafts. This can be found by subtracting the number of students enrolled in both painting and crafts from the total number of students in crafts:

\[ \text{Number of students enrolled only in crafts} = A - (P \cap A) = 18 - 7 = 11 \]

Next, we calculate the probability that a randomly chosen student is enrolled only in crafts. The probability \( P(E) \) of an event \( E \) is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

\[ P(\text{only in crafts}) = \frac{\text{Number of students enrolled only in crafts}}{\text{Total number of students}} = \frac{11}{40} \]

So, the probability that a randomly chosen student is enrolled only in crafts is \( \frac{11}{40} \).

Would you like more details or have any questions about this solution? Here are 5 additional questions you might consider:

1. What is the probability that a randomly chosen student is enrolled in painting?
2. How many students are enrolled only in painting?
3. What is the probability that a student is enrolled in both painting and crafts?
4. How many students are enrolled in neither painting nor crafts?
5. What is the probability that a student is enrolled in at least one of the courses?

**Tip:** When solving probability problems, it’s helpful to draw a Venn diagram to visualize the relationships between different groups.

Explore the probability of selecting a student who is enrolled only in crafts from a group of 40 students. Understand how to apply set theory and probability concepts to solve this problem. Suitable for high school students.

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