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# Problem 5. Let E, F, G be events in a probability space with sample space S and probability law Pr(), which satisfy Pr(EFG) Pr(EFG)

## Problem 5. Let E, F, G be events in a probability space with sample space S and probability law Pr(), which satisfy Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 1,4 Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 0. Prove the following statements. (a) Show that the above conditions are valid by showing that the above events are mutually exclusive and their union is S. (b) E and F are independent. (c) E and G are independent. (d) F and G are independent. (e) E, F, G are not independent.

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### Step: 1

a Lets denote the given events are as follows A EFGc B EFcG C EcFG D EcFcGc We know that PrA PrEFGc 1 PrB PrEFcG 1 PrC PrEcFG 1 PrD PrEcFcGc 1 and PrEFG0 PrEFcGc0 PrEcFGc0 PrEcFcG0 To show the events ...### Get Instant Access to Expert-Tailored Solutions

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### Step: 2

### Step: 3

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