Define : Addition Theorem of Probability. -Maths 9th

Define : Addition Theorem of Probability. -Maths 9th
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(a) For Two Events. If A and B are two events associated with a random experiment, then P(A ∪ B) = P(A) + P(B) – P(A ∩ B) ⇒ P(A or B) = P(A) + P(B) — P(A and B) Corollary 1: If A and B are mutually exclusive events, then, P(A ∩ B) = 0, therefore P(A ∪ B) = P(A) + P(B) Corollary 2: P(A or B) ≤ P(\(\underline{A}\)) + P(B) Given, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Since, P(A ∩ B) is greater than or equal to 0, P(A or B) < P(A) + P(B) Equality in the above result holds when A and B are mutually exclusive as P(A ∩ B) = 0(b) For three events If A, B and C be any three events associated with a random experiment, then P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) – P(B ∩ C) + P(A ∩ B ∩ C) Corollary 1: If A, B and C are mutually exclusive events, then P(A ∩ B) = P(B ∩ C) = P(A ∩ C) = P(A ∩ B ∩ C) = 0 ∴ P(A ∪ B ∪ C) = P(A) + P(B) + P(C)Note : (i) If A and B are two events such that A ⊆ B, then P(A) ≤ P(B) (ii) If E is an event associated with a random experiment, then 0 P(E) ≤ 1
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