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# Venny Venny AMy GMy | ISI MStat 2016 PSB Problem 3 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.

## Problem - Venn diagram and AM GM inequality

For any two events and , show that ## Solution

#### Draw the Venn Diagram

P(region Red) = P(region Blue) = P(region Grey) = P(region Brown) = Observe that . .

#### Now, Calculate Given Probability of Sets in terms of  . . . . .

#### The Final Inequality . .

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.

## Problem - Venn diagram and AM GM inequality

For any two events and , show that ## Solution

#### Draw the Venn Diagram

P(region Red) = P(region Blue) = P(region Grey) = P(region Brown) = Observe that . .

#### Now, Calculate Given Probability of Sets in terms of  . . . . .

#### The Final Inequality . .

Observe that . by AM - GM Inequality. . .

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