Independence (statistics)

Probability theory talks about events which occur with a given (possibly unknown) probability. Sometimes, when it talks about several events occurring, it assumes that if one event occurs, this does not change the probability of the other events occurring. 
More specifically, two events formula_1 and formula_2 are called independent (written as formula_3), if the probability of formula_1 occurring is the same whether formula_2 is assumed to have occurred or not. Alternatively, formula_1 and formula_2 are independent precisely when the probability of them occurring together is equal to the product of their individual probabilities.
Abraham de Moivre wrote: "Two events are independent, when they have no connexion one with the other, and that the happening of one neither forwards nor obstructs the happening of the other."