Mixture models are surprisingly common and addition/subtraction are not limited to mutually exclusive events. In such cases one goes the route of inclusion/excl

Mixture models are surprisingly common and addition/subtraction are not limited to mutually exclusive events. In such cases one goes the route of inclusion/exclusion formula. Summation is so fundamental to probabilities that it is how probabilities are even defined axiomatically in the Kolmogorov system. https://en.wikipedia.org/wiki/Sigma_additivity https://en.wikipedia.org/wiki/Sigma_additivity I think what you meant was that in computation one often needs to multiply probabilities and in such cases it is helpful to work in the log semiring https://en.wikipedia.org/wiki/Log_semiring https://en.wikipedia.org/wiki/Log_semiring