Two integers between \(1\) and \(100,\) inclusive, each randomly and independently chosen, are either added or multiplie

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Two integers between \(1\) and \(100,\) inclusive, each randomly and independently chosen, are either added or multiplied, with an equal chance of either operation. What is the probability that the result is even?

(A) \(\dfrac13\)

(B) \(\dfrac12\)

(C) \(\dfrac58\)

(D) \(\dfrac23\)

(E) \(\dfrac78\)

Answer: C

Source: Manhattan GMAT