Solution
= Solution
Apply the position version of the <Born rule> to the normalized <wavefunction>:
$$
\boxed{\Pr(0\le x\le L/3)=\int_0^{L/3}|\Psi(x)|^2dx=\frac3{L^3}\left[\frac{x^3}{3}\right]_0^{L/3}=\frac1{27}\simeq0.0370.}
$$
The result is independent of $L$ because the state and the measurement interval scale together. Most <position probability> lies towards the right wall, since the <probability density> grows as $x^2$.