Mathematica(@mathemetica):Probability quantifies likelihood from 0 (impossible) to 1 (certain). P(event) = favourable ÷ total outcomes. Diagrams show A ∪ B, A ∩ B, A' with P(not A)=1−P(A), A only=A∩B'. Mutually exclusive: A∩B=∅. Addition: P(A∪B)=P(A)+P(B)−P(A∩B). Independent: P(A∩B)=P(A)×P(B). Theoretical die P(5)=1/6≈0.1667; experimental from trials. Expected=P×trials. Sample space e.g. {1,2,3,4,5,6}. Stats: range=max−min, IQR=Q3−Q1 (middle 50%), mode most common, mean average, median middle, outliers distant. Actuaries set insurance premiums using claim probabilities from past data.

2026.07.25 09:14

Probability quantifies likelihood from 0 (impossible) to 1 (certain). P(event) = favourable ÷ total outcomes. Diagrams show A ∪ B, A ∩ B, A' with P(not A)=1−P(A), A only=A∩B'. Mutually exclusive: A∩B=∅. Addition: P(A∪B)=P(A)+P(B)−P(A∩B). Independent: P(A∩B)=P(A)×P(B). Theoretical die P(5)=1/6≈0.1667; experimental from trials. Expected=P×trials. Sample space e.g. {1,2,3,4,5,6}. Stats: range=max−min, IQR=Q3−Q1 (middle 50%), mode most common, mean average, median middle, outliers distant. Actuaries set insurance premiums using claim probabilities from past data.