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This problem is a very basic and cute application of set theory, Venn diagram and AM GM inequality to solve the ISI MStat 2016 PSB Problem 3.

For any two events and , show that

- Set Theory and Venn Diagram
- Basic Probability Theory
- AM - GM Inequality

P(region Red) =

P(region Blue) =

P(region Grey) =

P(region Brown) =

Observe that . .

.

.

.

.

.

.

Observe that .

by AM - GM Inequality.

.

.

Hence,

This problem is a very basic and cute application of set theory, Venn diagram and AM GM inequality to solve the ISI MStat 2016 PSB Problem 3.

For any two events and , show that

- Set Theory and Venn Diagram
- Basic Probability Theory
- AM - GM Inequality

P(region Red) =

P(region Blue) =

P(region Grey) =

P(region Brown) =

Observe that . .

.

.

.

.

.

.

Observe that .

by AM - GM Inequality.

.

.

Hence,

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