Mind-bending probability paradoxes, survivorship bias, Bayes theorem, and surprising statistical truths backed by data.
Our intuition compares 23 against 365 days, but statistics checks all 253 possible pairs between people—pushing the match probability to 50.7%.
Returning WWII planes had dense bullet holes on their wings and tails—so mathematician Abraham Wald urged armoring the unblemished engines instead.
After you pick 1 of 3 closed doors and the host reveals an empty door, switching to the remaining door jumps your win probability to 2/3.
From river lengths to city populations and tax filings, the leading digit '1' appears 30.1% of the time, while '9' shows up only 4.6%.
A treatment can outperform another inside every separate patient subgroup—yet look worse overall once all rows are pooled together.
If a condition affects only 1 in 10,000 people and a test has 99% sensitivity and 99% specificity (a 1% false-positive rate), testing positive gives just ~1% true odds of having it.
In 1913 at Monte Carlo, black hit 26 spins in a row while gamblers bet millions on red—forgetting that independent trials have zero memory.
In 1950, the US Air Force found that not a single pilot fell within the middle 30% 'average' range across all 10 physical dimensions at once.
Two charts climbing in near-perfect lockstep proves correlation, not causation—often driven by a hidden third variable like summer heat.
In any Gaussian normal distribution, 68% of data sits within 1 standard deviation, 95% within 2, and a massive 99.7% within 3.
