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).
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).
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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Question
![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ad229d2-94c2-4360-b0ca-273c76ee826c%2Fa1b2dbe6-ead0-449a-9c36-0f3cfe5f4f76%2Fvdg89t4_processed.png&w=3840&q=75)
Transcribed Image Text: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).
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