-8. a. Show that if A and B are independent, then P(A|B) = P(A). b. Say we have sets A, B, and C (do not assume independence). Show that P(AN Bn C) = %3D P(A|BNC)P(B|C)P(C).
-8. a. Show that if A and B are independent, then P(A|B) = P(A). b. Say we have sets A, B, and C (do not assume independence). Show that P(AN Bn C) = %3D P(A|BNC)P(B|C)P(C).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![8. a. Show that if A and B are independent, then \( P(A|B) = P(A) \).
b. Say we have sets A, B, and C (do not assume independence). Show that
\[ P(A \cap B \cap C) = P(A|B \cap C)P(B|C)P(C). \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2db349d-44e2-4dc0-ad50-be44fa6802da%2F24a1d060-e4bc-4c58-947e-01451764baa8%2Fmnfp71k_processed.png&w=3840&q=75)
Transcribed Image Text:8. a. Show that if A and B are independent, then \( P(A|B) = P(A) \).
b. Say we have sets A, B, and C (do not assume independence). Show that
\[ P(A \cap B \cap C) = P(A|B \cap C)P(B|C)P(C). \]
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