Statistics, data and evidence · Scope

What does a probability mean when an event happens only once?

A fair coin lands heads half the time over many throws. But what does it mean to say there is a 30% chance a particular election goes one way? This question asks whether probabilities describe the world, our knowledge of it, or both.

Claims

A probability for a single event measures how strongly the evidence supports it, and such probabilities can be checked over many forecasts: of all the events called '30%', about 30% should happen.
Probability lets us act sensibly under uncertainty, which is knowledge even if it is not certainty.

Counterclaims

When a single forecast 'fails', people often conclude the forecaster was wrong, so probabilities are easily misunderstood and may give an illusion of knowledge.
Different reasonable models give different probabilities for one-off events, so the number may say more about the modeller than the world.

Real-life situations from mathematics

Election forecasts in 2016

Before the 2016 US presidential election, the forecasting site FiveThirtyEight gave Donald Trump roughly a 29% chance of winning. When he won, many people said the forecast had been wrong, although events with a 29% chance happen often.

Weather forecasts

A forecast of a 70% chance of rain is judged by checking, over many days, whether it rained on about 70% of the days with that forecast.

Check dates and figures in a reliable source before you use them, and cite that source.

Use this in your TOK work

Essay. Fits titles about uncertainty, prediction or how we evaluate experts.

Exhibition. A betting slip or a forecast graphic with a percentage is a striking object for a prompt about certainty.

Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.

Themes and study heading

Knowledge and the knower Knowledge and politics Scope

What mathematics is about, and where its edges lie.