<Tr> <Td> A given B </Td> <Td> P (A ∣ B) = P (A ∩ B) P (B) = P (B A) P (A) P (B) (\ displaystyle P (A \ mid B) = (\ frac (P (A \ cap B)) (P (B))) = (\ frac (P (B A) P (A)) (P (B))) \,) </Td> </Tr> <Table> <Tr> <Td> </Td> <Td> This section needs expansion . You can help by adding to it . (April 2017) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This section needs expansion . You can help by adding to it . (April 2017) </Td> </Tr> <P> In a deterministic universe, based on Newtonian concepts, there would be no probability if all conditions were known (Laplace's demon), (but there are situations in which sensitivity to initial conditions exceeds our ability to measure them, i.e. know them). In the case of a roulette wheel, if the force of the hand and the period of that force are known, the number on which the ball will stop would be a certainty (though as a practical matter, this would likely be true only of a roulette wheel that had not been exactly levelled--as Thomas A. Bass' Newtonian Casino revealed). This also assumes knowledge of inertia and friction of the wheel, weight, smoothness and roundness of the ball, variations in hand speed during the turning and so forth . A probabilistic description can thus be more useful than Newtonian mechanics for analyzing the pattern of outcomes of repeated rolls of a roulette wheel . Physicists face the same situation in kinetic theory of gases, where the system, while deterministic in principle, is so complex (with the number of molecules typically the order of magnitude of the Avogadro constant 7023602000000000000 ♠ 6.02 × 10) that only a statistical description of its properties is feasible . </P>

Probability values are assigned on a scale of