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.