Question

Consider the probability space (,F, P) and events A and B. Recall that Ac

is the event such that A\Ac = ; and A[Ac = . By partitioning appropriate

sets into disjoint subsets and using the result from 1a, carefully prove;

i. P(Ac) = 1 − P(A),

ii. P(Ac \ B) = P(B) − P(A \ B),

iii. P(A [ B) = P(A) + P(B) − P(A \ B),

iv. P((A [ B) \ (Ac [ Bc)) = P(A) + P(B) − 2P(A \ B).

Answer 1

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