Ten Tastings and a Strict Alpha

A taster claims she can tell brand A from brand B. She is given $n = 10$ independent blind trials, each with two cups. Under the null hypothesis she is guessing:

$H_0: p = 0.5 \qquad H_1: p > 0.5$

so the number of correct calls $X$ follows $X \sim \text{Binomial}(10,\ 0.5)$.

She gets 9 of the 10 trials right. The lab uses a strict significance level of $\alpha = 0.01$.

Useful values: $\binom{10}{8} = 45$, $\binom{10}{9} = 10$, $\binom{10}{10} = 1$, and $2^{10} = 1024$.

What is the exact upper-tail p-value for this result, and what is the decision at $\alpha = 0.01$?