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SS2026/Quantum Computing/2. Probabilistic systems/Probabilistic Systems.md
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### Deterministic possibilities ### Deterministic possibilities
All the different possible outcomes. All the different possible outcomes.
Random two bit number has deterministic possibilities 00, 01, 10, 11. `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 coinflip 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 $d_i \geq 0$