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Chance and probability

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

When you roll a die you do not know beforehand which number comes. You learn how to calculate the probability (die Wahrscheinlichkeit) with Laplace's formula.
📄 Open worksheet (PDF, German)

The video

In the video we roll dice and count: favourable outcomes divided by possible outcomes.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:23 Outcome and event
  3. 0:44 Laplace's formula
  4. 1:18 The scale from 0 to 1
  5. 1:46 Careful, mistake!
  6. 2:06 Try it yourself

The most important points

Outcome and event

A die has \(6\) possible outcomes (die Ergebnisse). The event (das Ereignis) “even number” has \(3\) favourable outcomes: \(2, 4, 6\).

The favourable outcomes are coloured.
The favourable outcomes are coloured.

Laplace's formula

P = favourable outcomes : possible outcomes, if all outcomes are equally likely. \(P(6) = \frac{1}{6}\), \(P(\text{even}) = \frac{3}{6} = \frac{1}{2}\).

Three examples with the die.
Three examples with the die.

From 0 to 1

\(0\) means impossible, \(1\) means certain. A probability is always in between.

The scale from 0\,\% to 100\,\%.
The scale from \(0\,\%\) to \(100\,\%\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

A spinner has \(8\) equal fields: \(3\) red, \(1\) blue, \(4\) green. How big is a) \(P(\text{red})\) b) \(P(\text{green})\)?

Show solution

a) \(\frac{3}{8}\) b) \(\frac{4}{8} = \frac{1}{2}\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Zufall und Wahrscheinlichkeit (Ergebnis, Ereignis, Formel von Laplace). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.