In quantum mechanics, the solution of the equations (Schrodinger, Dirac...), called wave functions are deterministic, at each $\left(x,\,y,\,z,\,t\right)$ point, but the only prediction they give is a probability distribution, which depends on the boundary conditions of the problem. $Ψ$ is a complex valued function, and measurements are real numbers and this is the distribution of $Ψ^*Ψ$ (the absolute square or squared norm of $ψ$) which gives the probability of finding a particle at a given space time point.
Probabilities by definition means that many measurements in the same boundary conditions have to be carried out, and a comparison made between the predicted probability distribution and the measured one. So even though the distribution is strictly deterministic, its comparison with one datum is probabilistic.
Note the same boundary conditions statement. Once a measurement is carried out, the boundary conditions are different, a different $Ψ$ is needed for the system after the measurement, which is called a "collapse of the wavefunction". In experiments one does not observe the same particle scattering or decaying, but a large number of same boundary condition set ups to accumulate the probability distribution to compare.
Edit after comment:
By boundary conditions I mean the real numbers that have to be introduced so that the mathematical formula will give predictions for the specific observables of the experiment. For example the energy and momentum for getting the cross section from a scattering experiment of two protons, as in the LHC.