To check the correlation between Hidden Variable Theory and Quantum Mechanics, Bell calculated the expectation value
$$<\sigma_{e}(\vec a,\vec V) \sigma_{p}(\vec b,\vec V)> = \int d^n V \rho(\vec V) \sigma_{e}(\vec a,\vec V) \sigma_{p}(\vec b,\vec V)$$
Here I am assuming that "Alice" is measuring the spin of an electron e along $\vec a$ and "Bob" is measuring the spin of the positron $p$ along $\vec b$. Then $\sigma_{e}(\vec a,\vec V)$ and $\sigma_{p}(\vec b,\vec V)$ are the resulting spin values ($\pm \frac{1}{2}$) of the electron and positron, respectively. The vector $\vec V$ is an $n$-dimensional vector containing the hidden variables and $\rho(\vec V)$ is a probability distribution for the hidden variables.
But does this not assume QM is probabilistic? I thought Einstein disagreed with the probabilistc nature of Quantum Mechanics, as he said: I am convinced that He (God) does not play dice.