Raffle tickets numbered consecutively from 101 through 350…
The probability of an event is equal to: favorable outcomes/total outcomes
In this particular problem we have:
favorable outcomes = numbers with a hundreds digit of 2
total outcomes = consecutive integers from 101 through 350
Let’s start with the total outcomes. Although the word “inclusive” is not actually used, it is implied because we are told the raffle tickets start at 101 and end at 350. Thus, the number of tickets from 101 to 350, inclusive, is 350 – 101 + 1 = 250. (Note that we had to add 1 because we counted BOTH tickets 101 and 350.)
The favorable outcomes are the number of tickets with a hundreds digit of 2. Since all the numbers from 200 to 299 are included, there are 299 – 200 +1 = 100 numbers with a hundreds digit of 2.
Therefore, the probability that a randomly selected ticket with have a hundreds digit of 2 is 100/250 = 2/5.