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Show that if A, B, and C are mutually independent, then
Chapter 1, Problem 6E(choose chapter or problem)
PROBLEM 6E
Show that if A, B, and C are mutually independent, then the following pairs of events are independent: A and (B ∩ C), A and (B ∪ C), A' and (B ∩ C' ). Show also that A', B', and C' are mutually independent.
Questions & Answers
QUESTION:
PROBLEM 6E
Show that if A, B, and C are mutually independent, then the following pairs of events are independent: A and (B ∩ C), A and (B ∪ C), A' and (B ∩ C' ). Show also that A', B', and C' are mutually independent.
ANSWER:
Answer :
Step 1 of 4 :
Given, A, B and c are mutually independent events, then the following pairs of events are independent.
A and (, A and (, and (.
The claim is to show that , and are mutually independent.
We have to prove that
(a) P(= P(A) P(B) P(C)
(b) P( = P(A) P(BC)
(c) P( = P() P() P()