a) The inclusion-exclusion rule states that for any two events Ej and E2 P(Ε, η Ε2) = P(EI) + Ρ(Ε2) - P(E, UE2). Using i

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a) The inclusion-exclusion rule states that for any two events Ej and E2 P(Ε, η Ε2) = P(EI) + Ρ(Ε2) - P(E, UE2). Using induction, or otherwise, extend this result to n events: Ε (EUEig UEig 11<i2 1<i><i3 -... + (-1)-P(E, U...UEη). Hence deduce that = P(E, ... η En) -ΣΡ(Ε.) - ΣΡ(Ε, Ο Ει) + Σ Ρ(Ε, ΟΕ, U Eια) . = P(E, U...U En) - ΣΡ(Ε) - ΣΡ(Ε, η Ει) + Σ Ρ(Ε, η Ει, η Ει) =Ει (Ein Ein Eig) -... + (-1)*-1P(Ε, η...η Εη). 11<i2 11<><im