How does wave-particle duality explain the interference pattern?

Question

The screen is the Y axis and the line perpendicular to it is the X axis. We fire an electron with a well-defined momentum $p_x$ in the X direction. Shouldn't the x-co-ordinate of the particle follow a probabilistic distribution of wavelength $\frac{p_x}{h}$? Then how come we observe a probabilistic distribution along the Y axis instead (the screen)?

Answer 1

As soon as the electron meets the screen, you know its $x$ coordinate, so its $p$ is uncertain and so is its $y$ coordinate.