A bag contains 100 tickets numbered 1, 2, 3, .... 100. If a ticket is drawn out of it at random, what is the probability that the ticket drawn has the digit 2 appearing on it?

We will first look at the numbers that have 2 in the unit's digit.

So, the numbers between 1 to 100 having 2 in unit's place are 2, 12, 22, 32... 92. So, there are 10 such numbers.

For numbers having 2 at ten's place, we have numbers from 20 to 29. In total we have 10 such numbers.

But, 22 is common to both the groups, and hence, 

Total numbers with between 1 and 100 with digit 2 on it is 10+10-1=19.

Total sample space= 100.

So, required probability= $$\ \frac{\ 19}{100}$$