MathDB
14th Philippine Mathematical Olympiad 2011-National Stage #1

Source:

October 13, 2014
probabilitycombinatorics unsolvedcombinatorics

Problem Statement

A computer generates even integers half of the time and another computer generates even integers a third of the time. If aia_i and bib_i are the integers generated by the computers, respectively, at time ii, what is the probability that a1b1+a2b2++akbka_1b_1 +a_2b_2 +\cdots + a_kb_k is an even integer.