1994 AHSME Problem 27

A bag of popping corn contains \frac{2}{3} white kernels and \frac{1}{3} yellow kernels. Only \frac{1}{2} of the white kernels will pop, whereas \frac{2}{3} of the yellow ones will pop. A kernel is selected at random from the bag, and pops when placed in the popper. What is the probability that the kernel selected was white?

\textbf{(A)}\ \frac{1}{2} \qquad\textbf{(B)}\ \frac{5}{9} \qquad\textbf{(C)}\ \frac{4}{7} \qquad\textbf{(D)}\ \frac{3}{5} \qquad\textbf{(E)}\ \frac{2}{3}

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