Question

A person is asked to say a three digit number.
(i). What is the probability that all the three digits of this number are the same ?

Hint:

To find the total number of n-digit numbers, you can think about the choices for each digit. For a 3-digit number, the first digit can be any from 1-9 (9 choices), and the second and third can be any from 0-9 (10 choices each). Total = 9 × 10 × 10 = 900. This is a reliable method.

Answer 1

We need to find the probability of randomly choosing a three-digit number where all three digits are identical (e.g., 111, 222).

The probability of an event is calculated as:
P(Event) = Number of favorable outcomesTotal number of possible outcomes Total number of possible outcomes:
Three-digit numbers start from 100 and end at 999.
Total count = (Last number - First number) + 1
Total count = (999 - 100) + 1 = 899 + 1 = 900.
So, there are 900 possible three-digit numbers.

Number of favorable outcomes:
We are looking for numbers where all three digits are the same.
These numbers are: 111, 222, 333, 444, 555, 666, 777, 888, 999.
The number 000 is not a three-digit number.
So, there are 9 favorable outcomes.

Calculating the probability:
P(all digits are the same) = Favorable outcomesTotal outcomes = (9)/(900) Simplifying the fraction:
P(all digits are the same) = (1)/(100) The probability that all three digits are the same is (1)/(100).