I think you can do it, but you'd probably want to start with density matrices, or use the Heisenberg picture to keep your wavefunction super-simple. If we're talking to geniuses then maybe we can include a one-off statement, 'if det ρ = 0 so ρ = ψ ψ† for some "column vector" ψ, then the squared magnitudes of ψ's components are probabilities to be in that component's corresponding state.' to get the gist of it.