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We say every event must abide by the laws of nature, including QM probability/uncertainty. QM says outcomes are uncertain. Does uncertainty imply both randomness and probability? It seems that randomness is superfluous to the uncertainty principle, and it makes more sense to say only that uncertainty implies probability, and vice versa. Or are uncertainty and probability unrelated? According to Wiki they are:

Wiki: "One way to quantify the precision of the position and momentum is the standard deviation σ. Since is a probability density function for position, we calculate its standard deviation."

But there are other laws of nature we can use to test the viability of randomness. Here's a question/problem about randomness using conservation of momentum (CoM):

Particle A with mass Ma, moving at less than the speed of light in the X direction, hits particle B of mass Mb. The resulting velocity of particle B can be known using CoM.

If, instead, the resulting velocity of particle B was a distribution curve (uncertain), CoM would be violated.

Am I missing something here?