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If P(A₁) > 0 and if A2, A3, A4,... are mutually disjoint sets, show that P(A2 U A3 U ... |A₁) = P(A₂|A1) + P(A3|A1) + ··· ...

If P(A₁) > 0 and if A2, A3, A4,... are mutually disjoint sets, show that P(A2 U A3 U ... |A₁) = P(A₂|A1) + P(A3|A1) + ··· ...

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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If P(A₁) > 0 and if A2, A3, A4, are mutually disjoint sets, show that P(A₂ U A3 U... |A₁) = P(A₂|A1) + P(A3|A1) + ··· Hint: Use inclusion (exclusion) formula: P(C₁ U C₂ U... U Ck) = P₁ P2 + P3 + (−1)k+¹ pk, + P(Ck), ¤ P(C₁ n C₂) + P(C₁ n C3) + + P(C₂n C3) P3 = P(C₁ C3 N C3), P2 = P₁ = P(C₁) + P(C₂) + where p; is the probability of all possible intersections involving i probability sets
Transcribed Image Text:If P(A₁) > 0 and if A2, A3, A4, are mutually disjoint sets, show that P(A₂ U A3 U... |A₁) = P(A₂|A1) + P(A3|A1) + ··· Hint: Use inclusion (exclusion) formula: P(C₁ U C₂ U... U Ck) = P₁ P2 + P3 + (−1)k+¹ pk, + P(Ck), ¤ P(C₁ n C₂) + P(C₁ n C3) + + P(C₂n C3) P3 = P(C₁ C3 N C3), P2 = P₁ = P(C₁) + P(C₂) + where p; is the probability of all possible intersections involving i probability sets
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