2003 AMC 10A Problem 15

What is the probability that an integer in the set \{1,2,3,...,100\} is divisible by 2 and not divisible by 3?

\mathrm{(A) \ } \frac{1}{6}\qquad \mathrm{(B) \ } \frac{33}{100}\qquad \mathrm{(C) \ } \frac{17}{50}\qquad \mathrm{(D) \ } \frac{1}{2}\qquad \mathrm{(E) \ } \frac{18}{25}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.