Problem:
First is chosen at random from the set , and then is chosen at random from the same set. The probability that the integer has units digit 8 is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By observing the repeating pattern of the units digits of consecutive integral powers of we note that of the given values for a yield a units digit in of yield yield and yield . Similarly, the given values for yield of each of these units digits in . Thus there are possible pairs of units digits, and each pair is equally likely. Of these, three pairs, and , yield a sum with units digit . Thus, the desired probability is .