### Deterministic possibilities All the different possible outcomes. `Random two bit number has deterministic possibilities 00, 01, 10, 11.` ### Probability distribution A Probability for each possibility: Pr[x] = p where p $\in$ [0,1] `For a coin flip this would be Pr[Heads] = 1/2 and Pr[Tails] = 1/2` Combine all probabilities for all possible outcomes as vector to get probability distribution+ A valid distribution d has $\sum d_i = 1$ and for all i is $d_i \geq 0$ For a coin flip the probability distribution would be $d_coin \in \mathbb{R}^2$ with $d = (1/2, 1/2)^t$ ### Probabilistic processes A probabilistic process is a Matrix A $\in$ $\mathbb{R}^{N \times N}$ if every column of A is a valid probability distribution