Problem:
An integer , with , is to be chosen. If all choices are equally likely, what is the probability that at least one digit of is a 7 ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are 90 possible choices for . Ten of these have a units digit of 7, and nine have a tens digit of 7 . Because 77 has been counted twice, there are choices of for which at least one digit is a 7 . Therefore the probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions