# Calculate probability: formula and definition – What is the probability You can find out what is meant by probability here. There’s a definition for it to start with, and then we’ll look at probability formulas and examples. This topic belongs to the field of mathematics.

You are watching : What is the probability

Written by: Dennis Rudolph
Wednesday, March 07, 2018 at 21: 01 o’clock

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

• An explanation of what is meant by probability.
• Examples and formula to calculate them.
• Tasks / exercises so that you can practice this yourself.
• A video on the basics of probability.
• A question and answer section on this topic.

Tip: We’ll look at the basics of probability in a moment. It helps if you know what a random experiment is. If you don’t know, you can have a look here: Random experiment / random test.

## Explanation and definition of probability

Mathematics is mostly about calculating things very precisely:

• 2 + 3 = 5
• 8 – 2 = 6

But there are also things in life that cannot be calculated in this way. For example, if you roll a die, you don’t know for sure what the outcome will be (unless you cheat). If the outcome of an experiment – such as rolling a dice – is unclear, then you have arrived at an area of ​​mathematics known as probability calculation or stochastics.

Definition of probability:

Note:

Probability calculations (with the sub-area stochastics) are about specifying whether something is more likely to happen 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 quite 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.

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Typical random attempts:

Typical attempts to examine the probability are for example:

• Flip a coin.
• Throwing a die.
• Spin a wheel of fortune.
• Drawing a card (shuffled deck)

Experiments or attempts to “try out” the probabilities are called random tests or random experiments. We’ll look at some examples in the next section.

## Examples and formula Probability

This is an article on the basics of probability. So let’s just look at a very simple example. More sophisticated tests from this area are discussed in further articles.

Example 1: Toss a coin

We toss a coin. Either a number or a coat of arms can fall:

The probability of rolling a number is the same as the probability of rolling a crest. There are two possibilities for the outcome of the throw. One of these two possibilities occurs. The possible results are summarized in a result set. In this case it looks like this:

If all outcomes of the experiment have the same probability – which is the case here, as I said – then it is called a Laplace experiment.

Formula Laplace:

Where is:

• “P(E)” the probability of event E
• “E” the number of favorable outcomes
• “n” the number of possible results

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

Note:

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

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Task 1: If the probability of something is 0, what does it say?

• Sure to happen.
• Probably not.
• Probably occurs.
• Cannot enter.

You have successfully solved 0 of 4 tasks.

## Video probability

### Examples and explanation

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

• … which is a Laplace experiment.
• … which is a definition of a Laplace experiment.

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