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Math · Intermediate

Geometric Probability

When chance meets geometry, probabilities become areas and lengths. Estimate π by throwing random darts, repeat Buffon's 18th-century needle experiment, find the chance that a randomly broken stick forms a triangle, discover why "choose a random chord" has three different answers, and turn waiting and meeting times into areas.

7 lessons~35 min0/7 complete
Start courseHelpful background: Probability
1

Finding π by Chance

Darts and needles.

  1. Darts and πThe Monte Carlo method
  2. Buffon’s Needleπ from falling needles
2

Surprises

Sticks and chords.

  1. The Broken StickWill the pieces make a triangle?
  2. Bertrand’s ParadoxWhat does "random" mean?
3

Waiting and Meeting

Probability in time.

  1. The Meeting ProblemArrival times as a square
  2. The Waiting-Time ParadoxWhy the bus always seems late
  3. Random TrianglesHow often is a triangle acute?