Posted by Paige on Saturday, December 4, 2010 at 4:21am.
From 1 to 99 there are 10 + 9 = 19 with at least one 3. They are:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93,
and 30, 31, 32, 34, 35, 36, 37, 38, and 39
From 100 to 199 there are 19 with at least one 3.From 200 to 299 there are again 19.
From 300 to 399 there are 100 with at least one 3 (all of them).
Using similar arguments, there are 6*19 = 114 more with at least one 3.
The total is 252 and the probability of winning is 25.2%