# Principle of indifference

The principle of indifference (also called the principle of insufficient reason ) of probability theory states that in the case of distinguishable and mutually exclusive event possibilities, the probability of occurrence of each event without further information is to be set with ( Laplace probability, Laplace formula ), i.e. H. a discrete uniform distribution is assumed. ${\ displaystyle n> 1}$${\ displaystyle p = 1 / n}$

It was treated by Pierre-Simon Laplace in 1812 in his Théorie Analytique des Probabilités . The principle is based on the symmetry consideration, according to which the individual events, which in the sense of probability theory have the same properties, are interchangeable. Therefore, their probability of occurrence must also be the same.

The principle of indifference plays a central role in the treatises on logical probabilities . In Rudolf Carnap and Wolfgang Stegmüller (1958) it is formulated as follows: "If no reasons are known to favor one of various possible events, then the events are to be regarded as equally likely."

An example is the random experiment of drawing a ball with a number. There are three balls with the numbers 1 to 3. The random experiment now consists of pulling a ball from this set. The possible single events are:

• The drawn ball shows the number 1.
• The drawn ball shows the number 2.
• The drawn ball shows the number 3.

Since nothing more is known, the probability of the occurrence of each of the above events is to be set according to the principle of indifference . This also corresponds to the general feeling that with such a drawing the probability that a certain ball will be drawn is the same for all balls. ${\ displaystyle p = 1/3}$