What is the formula of the theoretical probability

Calculating Probabilities - Formula and Exercises

Math> Probability and Statistics

The concept of probability is in the probability calculationAs can be seen from the name, extremely important. The probability is a value that indicates how likely a certain one is event is. Very often we are concerned with probability when we are dealing with so-called Random experiments have to do.

In this tutorial we will look at which basic formula Probabilities (of random attempts) are calculated.

What are the probabilities?

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There are many different colored balls in a can. If we now pull out one of these balls at random, there are just as many possibilities to pull a certain ball as there are balls in the can. Each of the balls is a possible result of this random experiment, the chance for each of these results is the same. Instead of chance, one speaks of in mathematics probability.

If there were only one ball in the can, there would be only one possible outcome that would occur at $ 100 \% $.

However, if there are five balls in the can, there are five possible outcomes with equal probability. So the $ 100 \% $ is distributed over five possible outcomes. The probability for each of the five outcomes is therefore:

$ 100 \% ~: ~ 5 ~ = ~ 20 \% ~ = ~ 0.2 ~ = ~ \ frac {1} {5} $

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Calculating the probability

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In a random attempt, the number of results varies depending on the number of objects.

The Sum of all probabilities is $ 100 \% $ ($ ~ = ~ 1 $).

Are all possible outcomes equally likely, then the probability of one of these results applies:

$ \ Large {\ frac {1} {number of ~ all ~ possible ~ results}} $

In the general form one writes a $ n $ for the total number of all possible results. The probability of a result is therefore $ \ frac {1} {n} $.

Remember that you are using the probability as a Percentage, fracture or decimal number can specify.

Sample calculations

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When you toss a coin, two possible outcomes can occur: coat of arms or number. What is the likelihood of one of these outcomes?

We consider one of two possible outcomes. The probability of any of these outcomes applies:

$ \ frac {1} {2} ~ = ~ 0.5 ~ = ~ 50 \% $

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If we roll a six-sided die, there are six possible outcomes. What is the likelihood of one of these outcomes?

We consider one of six possible outcomes. The probability of any of these outcomes applies:

$ \ frac {1} {6} ~ = ~ 0.1667 ~ = ~ 16.67 \% $

Test your newly learned Knowledge in our Exercises!

Test your knowledge!

What is the basic formula for calculating probabilities?

How can probabilities be represented?

(There can be more than one answer)

What is a frequently used synonym for probability?

Express this probability as a decimal number: $ 56 \% $

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