Question 118
Suppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let $p$ be the probability that they can be labelled $A$ and $B$ so that $A$'s score on the General round is strictly greater than $B$'s, and $B$'s score on the Theme round is strictly greater than $A$'s. Estimate $P = \lfloor 10000 p \rfloor$.
An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{A}{E}, \frac{E}{A}\right)^{6}\right\rfloor$ points.
An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{A}{E}, \frac{E}{A}\right)^{6}\right\rfloor$ points.