The probability of an event and the probability of its complement always sum to 1.
In probability theory, when we talk about an event, we are referring to a specific outcome or set of outcomes in a given scenario. The complement of that event encompasses all the outcomes that are not part of the event. Given that the total possible outcomes in a probability space must cover all scenarios, the sum of the probabilities of an event (denoted as P(A)) and its complement (denoted as P(A’)) will always equal 1.
This can be mathematically expressed as:
P(A) + P(A’) = 1
For example, if the probability of rain tomorrow (event A) is 0.3, then the probability of it not raining (the complement of event A, A’) is 0.7. Adding these two probabilities together gives us:
0.3 + 0.7 = 1
This relationship is fundamental in probability theory and helps ensure that the probabilities within a defined space remain consistent and logically coherent.