AMC 8 1987 Problem 25

Ten balls numbered $1$ to $10$ are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is $\text{(A)}\ \frac{4}{9} \text{(B)}\ \frac{9}{19} \text{(C)}\ \frac{1}{2} \text{(D)}\ \frac{10}{19} \text{(E)}\ \frac{5}{9}$