**Unformatted text preview: **e space • We need a way of talking about “The outcome is one of a parAcular class.” • Combining events. – A or B is union – A and B is intersecAon – Not(A) is the complement Examples • Everyone has systolic blood pressure above 200 mm mercury. • The ﬁrst person has systolic blood pressure of 120 mm mercury. • At least two people have systolic blood pressure below 100 mm mercury. Combining events •
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• A or B = B or A A and B = B and A (A and B) and C = A and (B and C) (A or B) or C = A or (B or C) A and (B or C) = (A and B) or (A and C) Not(A and B) = Not(A) or Not(B) Not(A or B) = Not(A) and Not(B) The Axioms of Probability • ProbabiliAes between 0 and 1 inclusive. – The point: not inﬁnite. • The sample space has probability 1 – Has to be something… • P(DISJOINT union) = sum of probabiliAes – (Disjoint means no overlap) – This is where everything really starts! – Inﬁnite sums or ﬁnite sums Probability is like “weight” • The weight of everything is 1 • The weight of two “disjoint” pieces is the sum of the weights. Our ﬁrst theorem • The probability of not(A) = 1 - probability(A) • Proof: – P(A or not(A)) • It’s P(the sample space)… so it’s 1 • It’s P(A) + P(not(A)) – Why? Because A and not(A) are disjoint. • So, 1 = P(A) + P(not(A)) • Which axioms did we use? A corollary • The...

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