The problem reads:

"Dari angka-angka 0, 1, 2, 3, ..., 9 dibentuk semua bilangan ratusan tiga-digit yang mungkin. Kemudian, dipilih sebuah bilangan secara acak dari semua bilangan yang terbentuk. Peluang terpilihnya bilangan yang ketiga digit penyusunnya sama adalah ...."

Translation:

From the digits 0, 1, 2, 3, ..., 9, all possible three-digit numbers are formed. Then, one number is randomly selected from all the numbers formed. The probability that the chosen number has all three of its digits being the same is ____.

Step 1: Total possible three-digit numbers

A three-digit number is defined as a number between 100 and 999. For these numbers:

• The first digit (hundreds place) cannot be 0. It must be chosen from 1, 2, ..., 9 (9 options).
• The second and third digits can each be chosen from 0 to 9 (10 options each).

Thus, the total number of three-digit numbers is: $9 \times 10 \times 10 = 900$

Step 2: Number of favorable outcomes

A number with all three digits the same (e.g., 111, 222, ..., 999) satisfies the condition. For such numbers:

• The hundreds, tens, and units digits are identical.
• The digit can be any value from 1 to 9 (since 0 cannot be in the hundreds place).

Thus, there are: $9 \text{ numbers with all three digits the same (111, 222, ..., 999).}$

Step 3: Probability calculation

The probability of selecting a number where all three digits are the same is given by: $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{9}{900} = \frac{1}{100}$

Final Answer:

The probability is: $\boxed{\frac{1}{100}}$

Would you like a more detailed explanation or have questions? 😊
Here are 5 related problems you could explore:

1. How many three-digit numbers have no repeated digits?
2. What is the probability of choosing a three-digit number where at least two digits are the same?
3. How many four-digit numbers can be formed from 0 to 9, where all digits are distinct?
4. What is the probability of selecting a three-digit number where the sum of the digits is even?
5. How many three-digit numbers have their digits in ascending order?

Tip: Always check the constraints of the first digit in probability problems involving numbers!