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:

Note:

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.

Display:

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:

Where:

  • "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.

Note:

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

Show:

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.