7 Counterintuitive and Non-intuitive Probability Problems

Author(s): Saankhya Mondal

Originally published on Towards AI.

Exploring Mind-Bending Scenarios Where Probability Challenges Our Expectations

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This article will explore seven fascinating probability problems that challenge intuition and lead to surprising results. Each problem will illustrate how our expectations can differ from reality. I’ll discuss the hidden principles behind these seemingly paradoxical scenarios. Let’s get started.

Image generated by author using GPT 4o

This problem is taken from the book “50 Challenging Problems in Probability— by Frederick Mosteller”. The question goes as follows.

To encourage Elmer’s promising career, his father offers him a prize if he wins (at least) two tennis sets in a row in a three-set series to be played with his father and the club champion alternately: father-champion-father or champion-father-champion, according to Elmer’s choice. The champion is a better player than Elmer’s father. Which series should Elmer choose?

Intuition says Elmer must pick father-champion-father because he gets to play against his father twice and the champion, a better player than his father once. The answer is incorrect.

Elmer must pick champion-father-champion to increase his chances of winning the prize. Here’s why.

Let the probability of beating the champion be c and the father be f. f > c. Elmer will win the prize if he wins two sets… Read the full blog for free on Medium.

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Published via Towards AI