Equation field guide
Probability: a quantified chance
Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.
P(rain) = 0.30
Events and values
P(A) denotes the probability of event A. A probability is a modelled proportion over many comparable trials, or a degree of belief under a specified statistical model.
Probability is bounded: 0 ≤ P(A) ≤ 1. A value of 0.30 can also be written as 30% or 3/10.
Combining events
The probability of “A or B” depends on whether they can happen together. In general, P(A ∪ B) = P(A) + P(B) − P(A ∩ B), so the overlap is not counted twice.
For independent events, P(A ∩ B) = P(A)P(B). Independence is an assumption, not something that can be inferred merely because two events have different names.
How to interpret a result
Probability concerns the model and the reference class. A 30% forecast does not mean it will rain lightly, or for 30% of the day; it means the defined event has probability 0.30 under the forecast model.
Check the event definition, the time window, and whether a probability is conditional. P(A|B) asks for the chance of A given that B is known.