Problem:
If a,b and c are three (not necessarily different) numbers chosen randomly and with replacement from the set {1,2,3,4,5}, the probability that ab+c is even is
Answer Choices:
A. 52
B. 12559
C. 21
D. 12564
E. 53
Solution:
The quantity ab+c will be even if ab and c are both even or both odd. Furthermore, ab will be odd only when both a and b are odd, so the probability of ab being odd is 53⋅53=259. Thus the probability of ab being even is 1−259=2516. Hence, the required probability is 2516⋅52+259⋅53=12559.