First solution:

Calculate the total number of numbers from 101 to 350: 350 – 101 + 1 = 351 – 101 = 250. A number with a hundreds digit of 2 includes any number from 200 to 299 exclusive. Calculate the number of numbers from 200 to 299: 299 – 200 + 1 = 300 – 200 = 100. The probability that a ticket selected at random from the box will have a hundreds digit of 2 is the ratio of these two numbers:
= .

Second solution:

Subtract 100 from every number in the statement. Now the problem is as follows: find probability that a ticket selected at random between numbers 101 – 100 = 1 and 350 – 100 = 250 has a hundreds digit of 2 – 1 = 1. There are 250 numbers from 1 to 250 and only 100 of them have a hundreds digit of 1. The probability is the ratio of these two numbers:
= .

Third solution:

Use a proccess of elimination. If you take into account the first number and the last number in the interval, there are 250 numbers from 101 to 350 (answer E is wrong). There are 100 numbers from 200 to 299 (answer D is wrong). Answer C is wrong because it is the result of both mistakes mentioned above. Read the statement carefully, the tickets are numbered from 101, not from 1 (answer B is wrong).

Strategy:

The wording of the statement can be changed easily without changing the meaning. Applying a standard framework whenever possible is the best way to solve the problem.

Useful formulas: