Coin flipping

The coin toss is the easiest true random experiment. In the idealized case, it has two outputs, heads or tails, their probabilities are equal in size, each with 50 %. Indeed, it is also possible that the lands on the coin edge. However, this is very rare. Depending on the coin is by the weight difference of the sides a minimum imbalance.

The random experiment finds its application often in sports, such as playing football or American football. The coin toss is used as a random mechanism with two-up, a game of chance that is offered in many Australian casinos. When Fuchsen a coin to a particular place must be thrown; However, this is a skill and not gambling.

In the card game of poker with the term coin flip (English for coin toss ) is referred to a situation in which two players are equally strong with leaves in the battle for the win.

Examples of real coin flips

• In a bet or gambling
• In football, the referee tosses a coin to decide which team gets to choose their own half of the field and which can run the offense. Previously, sometimes the winner was determined in a playoff game when, it was clear depending on the competitive order for extension or renewal of a repetition of the game no winner.
• In American football, the referee tosses a coin ( coin toss ), the team captain of the external team may predict the outcome ( heads or tails ). The team that wins the coin toss can decide if it first performs the kickoff, the enemy can be performed as the first kickoff, which selects the first defensible half or cancels this option for the second half. The other team is allowed to select one of the remaining options.
• On 24 March 1965, the collection was named the semi-finals of the European Cup Winners ' Cup by a coin toss in international football. After all 3 games (round, back and playoff plus extension 0:0; 0:0; 2:2 ) were considered undecided between 1 FC Köln and Liverpool and a penalty shootout was not yet provided, accused the Belgian referee Schout a coin. The first time you throw it remained, however, vertically stuck in the ground. In the second litter she ruled in favor of the English.

Application in probability theory

The coin toss is used in probability theory often as a simple prototype of a random experiment. It describes the experiment with the following model:

• Describes the possible outcomes of the experiment: The coin shows head ( K) or number (Z ).
• The probability distribution is defined by.
• The random variable is defined by and.

This is a discrete uniform random variable.

The model is also varied as follows as required:

• If the coin is not ideal ( but eg dovetailed ), so you put in deviation determined with a " head probability " between 0 and 1.
• The random variable is sometimes used with a general definition and, where a and b are two ( meaningfully different ) are real numbers.