yhteenlaskusäännön

Yhteenlaskusääntö, also known as the addition rule, is a fundamental concept in probability theory and combinatorics. It describes how to calculate the probability of the union of two events, meaning the probability that at least one of the events occurs. The rule states that the probability of event A or event B occurring is equal to the probability of A plus the probability of B, minus the probability of both A and B occurring. This can be expressed mathematically as P(A U B) = P(A) + P(B) - P(A ∩ B).

The subtraction of P(A ∩ B) is crucial because if events A and B are not mutually exclusive, meaning they can occur at the same time, their intersection's probability would be counted twice if only P(A) + P(B) were used. Mutually exclusive events are those that cannot occur simultaneously, in which case their intersection is empty and P(A ∩ B) = 0, simplifying the addition rule to P(A U B) = P(A) + P(B).

The addition rule is widely applied in various fields, including statistics, data analysis, and decision-making under uncertainty. It provides a systematic way to combine probabilities and understand the likelihood of combined outcomes. For example, when calculating the chance of drawing either a red card or a face card from a standard deck of playing cards, the addition rule is used to avoid double-counting the red face cards.