### Probability theory

A **probability** gives the ratio between the number of favorable outcomes and the number of possible outcomes

P(G) =number of favorable outcomes number of possible outcomes

##### Explanation

If you play with a dice and you want to throw a 6, you can calculate the probability for that with the help of combinations. Then you calculate the number of favorable outcomes as

· · · · ·

because you want none of the numbers 1, 2, 3, 4 or 5 but just one 6. The number of possible outcomes is

because there will be only one of the six possible numbers. The ürobability is therefore

##### Note

This calculation is cumbersome, but it does show the principle of the theory of probability using combinations. You can simplify this a lot by omitting the combinations that you do not want to have (so it is beneficial if they do not occur). Then you get

but of course, you can also directly write

because you see that right away.