. (20 points) Let E and F be two subsets within a sample space 2. a. Show that E=(EnF)U(En Fe) where Fe is the complemen

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20 Points Let E And F Be Two Subsets Within A Sample Space 2 A Show That E Enf U En Fe Where Fe Is The Complemen 1 (49.23 KiB) Viewed 10 times

. (20 points) Let E and F be two subsets within a sample space 2. a. Show that E=(EnF)U(En Fe) where Fe is the complement of F. b. Show that EnF and En FC are disjoint sets. c. Use the axioms of probability to show that Prob(E)= Prob(En F) + Prob(En FC). d. With the above steps as a model, prove the following result. Let A1, A2,, An be sets such that Aj nAk = 0 if j k and n UA₁ = S. i=1 Prove that for any set B we have that n Prob(B) = Prob(BnA;). j=1 Prob(A₁B) I e With this, prove Bayes's theorem, which in this case is the statement that Prob(BA₁)Prob(A₁) n Σ Prob(B|A,)Prob(A₁) j=1