I now understand why no one has been able to give me the formula for the probability density of the impact position of a particle on the screen when both slits are open. What is the case. On Wikipedia, in the article Double-slit experiment in the chapter Classic wave-optics formulation, the formula for the intensity is given. It reads as follows
$$\begin{align}
I(\theta)
&\propto \cos^2 \left [{\frac {\pi d \sin \theta}{\lambda}}\right]~\mathrm{sinc}^2 \left [ \frac {\pi b \sin \theta}{\lambda} \right]
\end{align}$$
where b is the width of the slits, d is the distance between the two slits and ##\theta## is the magnitude of the angle between the line from the midpoint between the slits and the position of impact on the screen and the line from the midpoint between the slits perpendicular on the screen. Since ##tan(\theta)=x/L##, where ##x## is the position of impact of the particle on the screen and ##L## is the distance between the midpoint between the two slits and the screen, we also have ##\theta = arctan(x/L)## and in this way one can derive an expression for the intensity of ##x##, ##I(x)## by replacing in the formula for ##I(\theta)## ##\theta## with ##arctan(x/L)##. To determine the final probability density function ##f(x)##, it must be possible to solve the integral of the formulas for ##I(\theta)## and ##I(x)##, which is not the case. As long as these integrals cannot be determined, the probability density function cannot be determined either. Therefore, no one is able to give the formula for the probability density function. But why does no one say that in this case it is not possible to give the formula for the probability density function?