Example 6. What is the probability that in a randomly chosen two-digit number, the digits are the same?
Solution. Two-digit numbers are the numbers from 10 to 99; there are 90 such numbers in total. Numbers with identical digits are 9 (these are the numbers 11, 22, 33, $44,55,66,77,88,99$). Since in this case $m=9, n=90$, then

$$
P(A)=\frac{9}{90}=0.1,
$$

where $A$ is the event "number with identical digits".