2002 AMC 8 Problem 21

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is

\text{(A)}\ \frac{5}{16} \qquad \text{(B)}\ \frac{3}{8} \qquad \text{(C)}\ \frac{1}{2} \qquad \text{(D)}\ \frac{5}{8} \qquad \text{(E)}\ \frac{11}{16}

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