## Probability Theory - An Introduction

Preliminary definition:

The word “probability” denotes the chance that some result will occur.

Example:

When a coin is tossed, only two results can occur: “heads” or “tails”. When people ask what the probability of “tails” is during a coin toss, they are referring to the chances of “tails” occurring during.

In the example that uses a coin (and also in the example below that uses dice), the probability is actually known in advance. This is due to the physical form of the coin, which results in each side having an identical chance (0.5) of occurring (when throwing the dice, each side has a 1/6th chance).

When we toss a coin or a die a number of times, then we obtain a sample, and we can calculate the relative frequency of each result. The relative frequency can be calculated only after the coin or die has been tossed. Before the toss, we know only the probability, which reflects the theoretically projected relative frequency.

In other words, the probability is obtained from a theoretical calculation.

There are many more examples where the probability is the result of a theoretical calculation, such as the chance of winning a lottery.

Probability vs. Reality:

In order to gain a sense of what probability means, we will present several examples and we will examine the probability results obtained on the basis of a theoretical calculation.