Build a feel for unlikely
Probability & Big Numbers
Learn outcomes, bias, independence, powers of two, guessing work, and why collisions arrive much earlier than a full search.
5 instruments
One claim, three lenses.
Change depth inside any card. “Another example” adapts the lens to the situations you chose during onboarding.
One idea · three lenses
Start with all the ways it could happen
A fair six-sided die has six possible faces and each gets one equal share of the chance. Two dice have 36 ordered pairs, but some totals appear in more pairs than others. Seven is common because six different pairs make it.
One idea · three lenses
Fair once does not mean fair together
A coin can land heads half the time but still alternate head, tail, head, tail forever. Its balance looks right, yet after one flip you know the next. Good randomness needs attention to patterns between results too.
One idea · three lenses
Every fair bit doubles the maze
One fair yes-or-no choice makes two paths. A second makes four, then eight, then sixteen. The maze grows by doubling, so adding ten fair bits makes about a thousand times as many destinations.
One idea · three lenses
Clues shrink the hiding places
Guessing a card from a full deck is hard. Hearing “it is red” removes half the deck. Seeing earlier cards removes more. Probability changes when the guesser learns something.
One idea · three lenses
Matches happen sooner than one exact guess
Finding someone with your birthday may take a large crowd. Finding any two people who share a birthday takes surprisingly few, because every pair is another chance to match.
Bench notes
Keep these three.
- 01
Equal frequencies do not prove independence or unpredictability.
- 02
Each fair bit doubles a uniform candidate space.
- 03
Any-pair collisions become likely near the square root of the space.
Local field-note progress
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