What is the theoretical probability of a computer choosing a 2 digit number between 1 and 100 whose ones digit is greater than the tens digit?

Answer 1

lead digit
9, then 8 numbers, e.g. 98 97 96 95 94 93 92 91
8, then 7 numbers
...
2 , then 1 number
number of cases = 9+8+7+6+5+4+3+2+1 = 45

so prob = 45/99 = 5/11