Session-02

Bayes' Theorem Decoded Using a Real Business Survey

Last class ended with $P(A \cap B) = P(A) \cdot P(B)$ as the definition of independence. But does this definition imply symmetry? That is, if $A$ is independent of $B$, is $B$ automatically independent of $A$? Try to prove or disprove this before Ajay shows the two-line proof, and think about why dependence does not imply causation.

The proof is immediate: $P(B|A) = P(A \cap B)/P(A) = P(A)P(B)/P(A) = P(B)$, so independence is symmetric by definition. A critical insight follows: two variables can be statistically dependent without any causal link. Now we are ready to reverse the conditioning arrow using a real NPS survey tree.

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The Answer is 1/3 Not 1/2 — And We Can Prove It Live - The 2 Children Paradox

Bayesian Updating: How Each New Clue Shifts Your Beliefs