Angry Elephant Dessert

2025-09-15

Problem

You recently adopted a pet elephant and noticed he's been stomping nonstop since arriving at your house.

After careful observation, you discover he's creating an infinitely long sequence made up of two distinct stomps: right foot stomps and left foot stomps.

In any given position of the sequence, the probability of the stomp being a right foot stomp is $p$ (where $0 < p < 1$), while the probability of a left foot stomp is $1-p$.

How can you use this random sequence of stomps to derive the value of $\pi$?

Solution

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