1992 AHSME Problem 29

An "unfair" coin has a 2/3 probability of turning up heads. If this coin is tossed 50 times, what is the probability that the total number of heads is even?

\text{(A) } 25\left(\frac{2}{3}\right)^{50}\quad \text{(B) } \frac{1}{2}\left(1-\frac{1}{3^{50}}\right)\quad \text{(C) } \frac{1}{2}\quad \text{(D) } \frac{1}{2}\left(1+\frac{1}{3^{50}}\right)\quad \text{(E) } \frac{2}{3}

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