Question 158
For each $i \in \{1, \ldots, 10\}$, $a_{i}$ is chosen independently and uniformly at random from $[0, i^{2}]$. Let $P$ be the probability that $a_{1} \lt a_{2} \lt \cdots \lt a_{10}$. Estimate $P$.
An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{E}{P}, \frac{P}{E}\right)\right\rfloor$ points.
An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{E}{P}, \frac{P}{E}\right)\right\rfloor$ points.