If X is to be chosen at random from the integers between 1 to 5, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?  Choose the correct choice from the following answers:  A) 1/2  B) 2/3  C) 3/4  D) 4/5  E) 5/6
X+Y will be even if X and Y are both even or both odd.   P(X and Y are both even) = 2/5*2/4 = 1/5   P(X and Y are both odd) = 3/5*2/4 = 3/10   P(X+Y is even) = 1/5 + 3/10 = 1/2   The answer is 1/2.
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If X is to be chosen at random from the integers between 1 to 5, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?