Suppose that P(A)=0.3, P(B)=0.2, and P(C)=0.1. Further, P(AUB)=0.44, P(A^cC)=0.07, P(BC)=0.02, and P(AUBUC)=0.496. Decide whether A, B, and C are mutually independent. Exercise 2.52. Suppose that P(A) = 0.3, P(B) = 0.2, and P(C) = 0.1. Further,P(AUB) = 0.44, P(A°C) = 0.07, P(BC) = 0.02, and P(AUBUC) = 0.496. Decidewhether A, B, and C are mutually independent.

Answered: Suppose that P(A)=0.3, P(B)=0.2, and…

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Suppose that P(A)=0.3, P(B)=0.2, and P(C)=0.1. Further, P(AUB)=0.44, P(A^cC)=0.07, P(BC)=0.02, and P(AUBUC)=0.496. Decide whether A, B, and C are mutually independent.

Exercise 2.52. Suppose that P(A) = 0.3, P(B) = 0.2, and P(C) = 0.1. Further,
P(AUB) = 0.44, P(A°C) = 0.07, P(BC) = 0.02, and P(AUBUC) = 0.496. Decide
whether A, B, and C are mutually independent.

Expert Solution

Step 1

Given :

P(A) = 0.3, P(B) = 0.2, and P(C) = 0.1

P(A U B) = 0.44, P(A^c C) = 0.07, P(BC) = 0.02, and P(A B C) = 0.496

Now we have to check whether A,B and C are mutually independent

Three events A , B , and C are mutually independent if and only if the following two conditions hold:

The events are pairwise independent. That is, P ( A ∩ B ) = P ( A ) × P ( B ) and... P ( A ∩ C ) = P ( A ) × P ( C ) and... P ( B ∩ C ) = P ( B ) × P ( C )
P ( A ∩ B ∩ C ) = P ( A ) × P ( B ) × P ( C )

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