proportionality

Definition: two events are incompatible if they cannot occur at the same time

Ex: in experiment 2, event A: "we get 6" and event B: "we get 3" are incompatible

Property: when two events are incompatible, the probability that one or the other will occur is equal to the sum of their probabilities

Ex: in experiment 2, the event C: "we get 6 or we get 3" is

p (C) = p (A) + p (B) = 16 + 16 = 13

Definition: the opposite event of an event A is the one which occurs when A does not occur. We denote it A ("A barre")

Ex: in experiment 2, ie event D: "we get 3". The opposite event D can be written: "we do not get 3"

Property: the sum of the probabilities of an event A and its opposite is 1 p (A) + p (A) = 1

15 Ex: calculate the probability of the opposite event of D, p (D) = 1 - p (D) = 1 - 6 = 6