Problem:
Each integer through is written on a separate slip of paper and all nine slips are put into a hat. Jack picks one of these slips at random and puts it back. Then Jill picks a slip at random. Which digit is most likely to be the units digit of the sum of Jack's integer and Jill's integer?
Answer Choices:
A.
B.
C.
D.
E. each digit is equally likely
Solution:
From the units digits of the addition table of through (shown to the right) one sees that appears times and every other digit appears times.
Note 1. This table is called the "mod " addition table. Usually a row and a column are also included.
Note 2. Since there are sums of two positive digits, the units digits cannot be equally likely. This rules out .