We know that if two or more events are independent of each other then the probability of happening of both is simply the product of individual probabilities , i was thinking if its possible to show/prove it using just the venn diagram of the possible events taking place ? How the individual multiplication being arrived that i would like to get from the Venn diagram .
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1You may want to make a "rectangle" type diagram like $$ \left[\begin{array}{cc} (1,3) & (4,3) & (8,3) & (3, 3)\\ (1,2) & (4,2) & (8, 2)& (3, 2) \\ (1,0) & (4, 0) & (8, 0) & (3, 0) \end{array} \right]$$ which can represent equally likely ordered pair outcomes $(X,Y)$ where the value of $X$ does not depend on the value $Y$. – Michael Apr 08 '22 at 16:57

1You probably do not want a Venn diagram to illustrate this, but something more like https://stats.stackexchange.com/a/380791/2958 – Henry Apr 08 '22 at 16:57

You need not only Venn diagram but power of each set in it (measured in equiprobable elementary events) to check independence. – Ivan Kaznacheyeu Apr 08 '22 at 16:59

Understood thanks @Michael , Henry , Ivan – Orion_Pax Apr 10 '22 at 09:17

1Please check out [Visualising independence of events](https://math.stackexchange.com/a/4225537/21813). – ryang Apr 13 '22 at 12:59

1Amazing explanation Sir thanks @ryang – Orion_Pax Apr 13 '22 at 15:17

@Orion_Pax Thanks, and you're welcome. And this elaborates on a point raised in the previous link: [Mutually exclusive typically implies dependence](https://math.stackexchange.com/a/4419308/21813). – ryang Apr 13 '22 at 15:59