a probability theorem I need help proving
so here is the theorem I need to prove:
P1, P2, P3, and P4 are mutually exclusive and jointly exhaustive propositions. Here is the theorem (X represents multiplication):
P(R/N&E) = P(R/N&E&P1) X P(P1/N&E) + P(R/N&E&P2) X P(P2/N&E) + P(R/N&E&P3) X P(P3/N&E) + P(R/N&E&P4) X P(P4/N&E)
I need to prove this for my probability theory class. This is a theorem used by Alvin Plantinga in his Evolutionary Argument Against Naturalism. According to Plantinga, the reliability of our own mind to grasp truths given naturalism and evolution is low (the second part of the course will be devoted to investigating Plantinga's argument). I need to understand the proof for this theorem so I can hopefully refute his nonsense.
Todangst or Philosophos, work your magic
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