AHSME 1973 Problem 23

There are two cards; one is red on both sides and the other is red on one side and blue on the other. The cards have the same probability (1/2) of being chosen, and one is chosen and placed on the table. If the upper side of the card on the table is red, then the probability that the under-side is also red is $\textbf{(A)}\ \frac14 \textbf{(B)}\ \frac13 \textbf{(C)}\ \frac12 \textbf{(D)}\ \frac23 \textbf{(E)}\ \frac34$