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Classic Probability Puzzles and Why They Trick Us
A tour of famous probability puzzles, from Monty Hall to the birthday problem, and the intuitive trap each one sets for even careful thinkers.
Foundations
Puzzles and Paradoxes
Famous probability puzzles and why intuition fails on them.
Bertrand Box Paradox
Three boxes, six coins and one gold draw: why the other coin in the box is gold with probability two thirds rather than one half, shown by simple counting.
Non-Transitive Dice Explained
Three six-sided dice where A beats B, B beats C and C beats A, each with probability 5/9. The face values are listed so you can check every pairing by hand.
Penneys Game: Why Some Coin Sequences Beat Others
In Penneys game two players pick coin-flip sequences and the second chooser gets the edge. See the three-flip version, the rule, and one case checked by hand.
Simpsons Paradox in Game and Sports Statistics
With illustrative win-rate numbers, see how a player can be better in every game mode yet look worse overall, and why combined statistics can reverse.
The Birthday Problem: Why 23 People Is Enough
Why a shared birthday among just 23 people has a probability of about 50.7 percent, worked out through the complement and the count of possible pairs.
The Boy or Girl Born on a Tuesday Puzzle
Why learning that one of two children is a boy born on a Tuesday changes the chance of two boys from one third to 13 out of 27, counted case by case.
The Monty Hall Problem Explained Step by Step
A full outcome table shows why switching doors wins two thirds of the time under the standard Monty Hall rules, and which assumptions the answer depends on.
The Secretary Problem and Optimal Stopping
How the 37 percent rule works for choosing the best option from a sequence seen one at a time, with a three-candidate example checked by hand.
The St Petersburg Paradox and Infinite Expectations
A coin game with an infinite expected payout that nobody would pay much to play: how the numbers work and the usual resolutions, from capped payouts to utility.
The Two Child Problem and Why Wording Matters
Why the chance of two boys is one third if you know at least one child is a boy, but one half if you know the older child is a boy: wording changes the answer.
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