Hypothesis Tests · Superchallenge problem

A fair coin is tossed 6 times to test $H_0\!: p = \tfrac12$ against $H_a\!: p > \tfrac12$, and the exact p-value $P(X \ge k)$ is reported, where $k$ is the observed number of heads. Since $H_0$ is true here, what is the probability that the reported p-value is at most $0.3$? Give a fraction.