Yhteenlaskusääntö

Yhteenlaskusääntö, also known as the addition rule, is a fundamental concept in probability theory. It provides a way to calculate the probability of the union of two events occurring. The rule states that the probability of event A or event B happening is the sum of their individual probabilities minus the probability of both events happening simultaneously. This can be expressed mathematically as P(A or B) = P(A) + P(B) - P(A and B).

A special case of the addition rule applies when the events are mutually exclusive. Mutually exclusive events are those that cannot occur at the same time. For example, rolling a 1 and rolling a 6 on a single dice roll are mutually exclusive. In such cases, the probability of both events happening, P(A and B), is zero. Therefore, for mutually exclusive events, the addition rule simplifies to P(A or B) = P(A) + P(B). This simpler form is particularly useful in scenarios where outcomes are distinct and non-overlapping.

The addition rule is crucial for understanding more complex probability calculations. It forms the basis for deriving other probability rules and is widely applied in various fields, including statistics, data analysis, and decision-making under uncertainty. Understanding this rule allows for accurate prediction and assessment of the likelihood of combined events.