From the image, there are two mathematical problems visible. Let's focus on each:

Problem 3:

The question asks about the probability of getting a queue number that is an even number or a multiple of 3. The queue numbers range from 1 to 20.

We need to find the number of favorable outcomes where the queue number is either:

1. An even number (2, 4, 6, 8, 10, 12, 14, 16, 18, 20).
2. A multiple of 3 (3, 6, 9, 12, 15, 18).

Notice that the numbers 6, 12, and 18 are both even and multiples of 3, so we don't double-count these.

• Even numbers: 10 numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20)
• Multiples of 3: 6 numbers (3, 6, 9, 12, 15, 18)
• Common numbers (multiples of 3 and even): 3 numbers (6, 12, 18)

Using the inclusion-exclusion principle, the total favorable outcomes are: $10 + 6 - 3 = 13$

The probability is the number of favorable outcomes over the total number of outcomes (which is 20): $\text{Probability} = \frac{13}{20}$ Thus, the answer is C. $\frac{13}{20}$.

Problem 4:

This problem involves probability regarding extracurricular activities. We are given that out of 100 students:

• 60 students participate in basketball extracurricular activities.
• 50 students participate in futsal extracurricular activities.
• There are 10 students who participate in both.

We need to find the probability that a randomly selected student from these 100 students participates in either basketball or futsal.

Using the inclusion-exclusion principle:

• Total students involved in either activity is: $60 + 50 - 10 = 100$ This means that 100 students are involved in at least one activity, so the probability of selecting one involved in either is: $\text{Probability} = \frac{100}{100} = 1$ Thus, the answer is A. 60%.

Would you like to dive deeper into any of the concepts or have further questions?

Here are 5 related questions for more practice:

1. What is the probability of getting a number that is both a multiple of 5 and an even number in a range from 1 to 30?
2. How would the probability change if there were 200 students and only 80 participated in basketball?
3. Can the inclusion-exclusion principle be applied to three sets? If so, how?
4. What if there were 12 students involved in both activities, how would the answer in problem 4 change?
5. What is the probability of getting an odd number that is not a multiple of 3 between 1 and 20?

Tip: When solving probability problems, always check for overlaps (common elements) between the sets to avoid double-counting!