8. Prove the following properties of conditional probability:a. P(|B) = 1, P (Ø|B) = 0;b. P(A₁ U A₂|B) = P(A₁|B) + P(A₂|B) – P(A₁A₂|B);P(A|B) = 1 - P(AB).

a) and Recall that the conditional probability of an event A given event B is defined as:where P(B)…

Answered: 8. Prove the following properties of…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 11CR

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8. Prove the following properties of conditional probability: a. P(|B) = 1, P(Ø|B) = 0; b. P(A₁ U A₂|B) = P(A₁|B) + P(A₂|B) - P(A₁A₂|B); P(A/B) = 1- P(AB).