What is the difference between biased and unbiased die ?

A biased die and an unbiased die are terms commonly used in the context of probability and statistics.

An unbiased die refers to a fair or regular die, which is designed to have equal probability for each of its possible outcomes. For example, a standard six-sided die is considered unbiased because it has an equal chance of landing on any of the numbers from 1 to 6. The probabilities are evenly distributed, and each face has a 1/6 chance of being rolled.

On the other hand, a biased die is one that is intentionally or unintentionally altered in a way that affects the probabilities of its outcomes. This alteration could be due to factors such as the shape, weight distribution, or imperfections in the manufacturing process. As a result, the probabilities of rolling each face are not equal. For instance, a biased six-sided die might have a higher probability of landing on a specific number, such as 6, compared to the other numbers.

The bias in a die can be quantified by examining the probabilities associated with each outcome. In the case of an unbiased die, the probabilities are uniform, while a biased die will have uneven or non-uniform probabilities.

It's important to note that unbiased dice are typically used in games and statistical analysis because they provide a fair and predictable outcome, whereas biased dice can introduce an element of uncertainty and unfairness.