Buffon’s needle explained from scratch: why a needle dropped on a plank floor crosses a crack with probability 2/π, solved two ways with geometric probability, plus how to estimate π by tossing needles.
Bertrand’s paradox: draw a random chord in a circle. Is it longer than a side of the inscribed triangle? Depending on what ‘random’ means, the answer is 1/3, 1/2 or 1/4.
Two friends arrive at random within an hour and wait 15 minutes each. What are the odds they meet? Map time to a square and the answer is the area of two triangles.
A small change to the broken stick problem quietly breaks the method that solved it — and a logarithm turns up where no logarithm should be.
A first look at geometric probability — where the answer turns out to be hiding inside an area.
