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​.