How many 2 digit numbers are there? From 10 to 99, there are 90 of them.

You also know that every other number is an odd number, so exactly half of the 90 numbers are odd numbers. 

So there are 45 odd 2-digit numbers.

Probability = (number of favourable events)/(number of total events possible)

Here total events possible = 90 (there are 90 possible 2 digit numbers)
Total favorable events = 45 (only 45 of the 2 digit numbers are odd)

So the probability = 45/90 = 1/2

Hope this helps :)