What is the probability that the two digits in a randomly selected two digit positive integer ( that is, an integer between 10 and 99) are the same?
If I understand your question:
How many integers are there between 10 and 99?
99 - 10 + 1 = 90 integers
How many 2-digit integers are there that are the same? Well, you have: 11, 22, 33, 44, 55, 66, 77, 88, 99 =9 integers
So, Probability of picking an integer with the same 2 digits =9 / 90 = 1 / 10.