Prove P(A’) = 1 - P(A)

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Prove P(A’) = 1 - P(A)

The sample space S contains an Event A and everything not A, called A'

We know P(S) = 1

P(S) = P(A U A')
P(A U A') = 1
P(A) + P(A') = 1

subtract P(A) from each side:
P(A’) = 1 - P(A)