A student and a professor choose a two digit number. Find the probability that the two choose the same number.

I'm not sure the best method to solve this or what the answer could be. I do know that it has to be between 10-99.

Thank you.

I talked with a friend that said there are 90 possibilities (10-99) and the student picks one two digit number and the professor picks one two digit number.

1/90 + 1/90= 2/90 and simplified would be ((1/45))that both choose a two digit number.

Is this correct?