Why is Bertrands paradox only met when t=0

Bertrand's paradox is a mathematical paradox that arises in probability theory. It states that there is no unique way to define the probability of an event in a circle, given only the information that the event is contained in the circle.

The paradox is only met when t=0 because at t=0, there is no unique way to define the event in the circle. This is because there are three possible types of events that can be defined: an arc, a chord, or a point. Each of these events has a different probability, and there is no unique way to choose which event to consider.

However, as t increases, the paradox disappears because the probability of each type of event becomes well-defined. For example, as t approaches infinity, the probability of a chord approaches 1/2, and the probability of an arc or a point approaches zero. Therefore, as t increases, the paradox disappears and the probability of an event in a circle becomes well-defined