Back to the library

Numbers and chance

Numbers and chance: a chapter of the Thinking Clearly Book, with the mind traps and tricks that are worth knowing by name.

10 cards · Science

Start learning

Each Zap teaches up to 5 new cards, so you learn the deck a few at a time.

Checked by the Brain Zap team · reviewed 26 Oct 2026

Sources: List of cognitive biases (Wikipedia), Fallacy (Stanford Encyclopedia of Philosophy)

Preview

  • Believing red is 'due' after a run of blacks

    Show answer: Believing red is 'due' after a run of blacks

    Gambler's fallacy

    Learn more: Each spin is independent, so past results don't change the odds of the next one.

  • Chance a fair coin lands heads after 5 tails in a row

    Show answer: Chance a fair coin lands heads after 5 tails in a row

    50%

    Learn more: Coins don't remember: each flip is a fresh 50–50, whatever came before.

  • The middle value once numbers are in order

    Show answer: The middle value once numbers are in order

    Median

    Learn more: That's why incomes and house prices are usually given as this rather than as the average.

  • Add them all up and divide by how many

    Show answer: Add them all up and divide by how many

    Mean

    Learn more: It's useful, but a single extreme value can drag it far from what's typical.

  • The value that appears most often

    Show answer: The value that appears most often

    Mode

    Learn more: It's the only average that works for things like favourite colours, not just numbers.

About this topic

Numbers can mislead as easily as words. A coin has no memory, an average can hide what's typical, a risk that 'doubles' may still be tiny, and a survey of ten people proves very little. A few simple ideas from statistics help you read headlines, test results and sales pitches without being fooled. Nobody is immune, experts included, but knowing the names makes the traps much easier to notice, in yourself as well as in others.

This is a chapter of the Thinking Clearly Book. Each card asks one question, with a hint before you answer and a short reason after. Once you know most of this chapter, the next one starts arriving in your Daily Zap.

All 10 cards

  1. Believing red is 'due' after a run of blacks

    Gambler's fallacy

    Learn more: Each spin is independent, so past results don't change the odds of the next one.

  2. Chance a fair coin lands heads after 5 tails in a row

    50%

    Learn more: Coins don't remember: each flip is a fresh 50–50, whatever came before.

  3. The middle value once numbers are in order

    Median

    Learn more: That's why incomes and house prices are usually given as this rather than as the average.

  4. Add them all up and divide by how many

    Mean

    Learn more: It's useful, but a single extreme value can drag it far from what's typical.

  5. The value that appears most often

    Mode

    Learn more: It's the only average that works for things like favourite colours, not just numbers.

  6. Risk goes from 1 in 10,000 to 2 in 10,000: the extra risk

    1 in 10,000

    Learn more: 'Doubles your risk' sounds scary, but the real rise is tiny: always ask 'out of how many?'

  7. Why a survey of 10 people tells you little

    The sample is too small

    Learn more: Small samples swing wildly by chance; bigger, random samples give results you can trust.

  8. Ignoring how common something is to begin with

    Base rate neglect

    Learn more: For a rare disease, even an accurate test gives many false alarms, as healthy people far outnumber the sick.

  9. Feeling better after a pill with nothing in it

    Placebo effect

    Learn more: That's why good trials compare a treatment with a dummy pill, without anyone knowing which is which.

  10. Extreme results tend to be followed by ordinary ones

    Regression to the mean

    Learn more: Luck plays a part in extremes, so the next result usually lands nearer the average, with no cause needed.

More science decks

Each deck takes about 1 min a day.

All science decks