What is the probability that the number chosen will have 2 as at least one of its digit?

Question

An integer from 299 through 1000 both inclusive, is to be chosen at random.
What is the probability that the number chosen will have 2 as at least one of its digit?

Answer 1

Number of integers 299-1000--> 702
Numbers with 2 are:
299 --> 1
302, 312, 322, ... , 392--> 10
402, 412, 422, ... , 492--> 10
502, 512, 522, ..., 592--> 10
602, 612, 622, ..., 692--> 10
702, 712, 722, ..., 792--> 10
802, 812, 822, ..., 892--> 10
902, 912, 922, ..., 992--> 10
Total number of integers with 2 --> 1+10+10+10+10+10+10+10=71
Probability--> 71/702=10.11%