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Let's solve the questions one by one.

### Question 1
Agung rolls a die 1,200 times, and the frequency of each outcome is recorded in the table:
- **Frequency for each side**:
  - 1: 180
  - 2: 240
  - 3: 195
  - 4: 195
  - 5: 180
  - 6: 210

The relative frequency of getting a 1 is calculated as:
\[
\text{Relative Frequency} = \frac{\text{Frequency of 1}}{\text{Total Rolls}} = \frac{180}{1200} = \frac{3}{20}
\]

So, the answer is **B. \(\frac{3}{20}\)**.

### Question 2
There are 10 pieces of paper numbered 1 to 10. If 2 are drawn randomly and their numbers are added, the probability of getting an odd sum is calculated as:

- Total ways to choose 2 pieces: \(\binom{10}{2} = 45\).
- Ways to get an odd sum:
  - Choose 1 even number and 1 odd number.
  - There are 5 odd numbers and 5 even numbers.
  - Combinations: \(5 \times 5 = 25\).

Probability:
\[
\frac{25}{45} = \frac{5}{9}
\]

So, the answer is **E. \(\frac{5}{9}\)**.

### Question 3
Pak Karno has a box with 60 fruits: 8 pears, 12 avocados, and the rest are guavas. The probability of drawing a guava:

- Number of guavas: \(60 - 8 - 12 = 40\).
- Probability:
\[
\frac{40}{60} = \frac{2}{3}
\]

So, the answer is **C. \(\frac{2}{3}\)**.

### Question 4
The diagram shows a spinner divided into 8 equal parts, numbered 1 to 8. The probability of the arrow pointing to a number greater than 5 (i.e., 6, 7, or 8):

- There are 3 favorable outcomes.
- Probability:
\[
\frac{3}{8}
\]

So, the answer is **C. \(\frac{3}{8}\)**.

### Question 5
The word "KALIMANTAN" has 10 letters, and the frequency of the letter "A" is 3. The probability of choosing an "A":

\[
\frac{3}{10}
\]

So, the answer is **C. \(\frac{3}{10}\)**.

Let me know if you'd like to delve into any question further. Here are five related questions to expand on this:

1. What is the expected value of rolling a weighted die given different probabilities?
2. How do you find the probability of getting a sum divisible by 3 when drawing two cards numbered 1 to 10?
3. If Pak Karno adds 10 more guavas to his collection, what is the new probability of selecting a guava?
4. What is the probability of landing on an odd number on the given spinner?
5. How would the probability change if the word was "MALAYSIA" instead of "KALIMANTAN"?

**Tip:** For probability questions involving "at least one" events, it is often easier to calculate the complement probability (i.e., "none") first and then subtract from 1.

This is a math-based problem set containing 8 multiple-choice questions related to probability, combinatorics, and relative frequency, aimed at high school students.

Explore a series of high school math problems covering topics like probability, combinatorics, and relative frequency. Learn how to calculate probabilities, solve combination problems, and find relative frequencies. Suitable for Grades 10-12 students.

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