Past exam of the physics A course of the University of Cambridge / 2022 / Paper 1 / Section A / 4

Let $M$ denote an incident muon and $S$ a detector signal. The selected sample is conditioned on $S$. The law of total probability givesBy Bayes' theorem, the contamination, namely the conditional probability that a selected particle is not a muon, isFor example, per $10000$ incident particles the expected selected counts are $8550$ true muons and $100$ other particles. The denominator is the $8650$ selected particles; the rejected muons are outside this sample.