Show that if A, B, and C are mutually independent, then

Chapter 1, Problem 6E

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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.

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()

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