Activity 3.4.2 What is the probability formula

Calculating probability: formula and definition

You can learn what the probability is and how to calculate it here. Let's look at this:

  • A Explanationwhat is meant by the term probability.
  • Examples and formula to calculate it.
  • Tasks / exercises so that you can practice this yourself.
  • A Video to the basics of probability theory.
  • A Question and answer area to this topic.

Tip: We'll look at the basics of probability calculus in a moment. To do this, it is helpful if you know what a random experiment is. If you don't know, you can take a look here: Random experiment / chance experiment.

Explanation and definition of probability

Most of the time, mathematics is about calculating things very precisely:

But there are also things in life that cannot be calculated in this way. For example, if you roll a dice, you are not sure what the outcome will be (unless you are cheating). If the outcome of an experiment - like throwing a dice - is unclear, then you have reached a field of mathematics that is known as probability calculation or stochastics.

Definition probability:


The calculation of probability (with the sub-area stochastics) is about indicating whether something is more likely or not. The probability is an indication between 0 and 1 (or between 0% and 100%). At 0 it is impossible for anything to happen. At 1 it is very certain that something will happen. The closer the number is to 1, the more likely something will happen. Or vice versa: the closer to 0, the less likely it is.

Typical random attempts:

Typical experiments in which one examines the probability are for example:

  • Tossing a coin.
  • Throwing a dice.
  • Spinning a wheel of fortune.
  • Draw a card (shuffled deck)

Experiments or attempts to "try out" the probabilities are called random experiments or random experiments. In the next section we look at some examples.


Examples and formula probability

This is an article on the basics of probability theory. So we're only looking at a very simple example. More sophisticated experiments in this area are discussed in further articles.

Example 1: tossing a coin

We flip a coin. Either number or coat of arms can be used:

The probability of throwing is the same as the probability of throwing a coat of arms. There are two possibilities for the outcome of the litter. One of these two possibilities occurs. The possible results are summarized in a result set. In this case it looks like this:

If all the results of the experiment have the same probability - which is the case here as I said - then one speaks of a Laplace experiment.

Formula Laplace:


  • "P (E)" is the probability of the event E
  • "E" is the number of favorable results
  • "n" the number of possible outcomes

In the case of the coin, we have 2 possible outcomes (number and coat of arms), so the denominator is 2. One of them stands for number or coat of arms. You can also represent this with a tree diagram. On this number and coat of arms are abbreviated with Z and W. The probability is 1/2 in each case.


If all possible test outcomes are equally likely, this is called the Laplace test. You can find more about this - for example with a cube experiment - under Laplace experiment / Laplace experiment.

Tasks / exercises probability


Video probability

Examples and explanation

We'll cover the basics of probability in the next video. You can see...

  • ... what a Laplace experiment is.
  • ... is the definition of a Laplace experiment.
  • ... we add tasks / examples to it.

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Questions with answers about probability

This section deals with typical questions with answers about probability.

Q: Where can I find more information on this topic?

A: Probability is just one of the fundamentals of probability theory. You can find this and other topics here:

Q: When is this topic covered in school?

A: The concept of probability is mostly dealt with in school from the 6th grade onwards. However, the topic also accompanies many pupils up to the 12th or 13th grade.