This equation is used when one sees the word "or" and ACP (Additive Counting Principle) is used because we are adding probabilities.
Ex. We would use this equation if a question asked: What is the probability that in a group of teachers we randomly select either a male or a female. [Basically a teacher cannot be a male and a female at the same time(as far as we know), so it is said that these two events are mutually exclusive.]

This equation is used when one sees the word "or" and events from A and B can happen at the same time. Again ACP is used because we are adding probabilities.
Ex. We would use this equation if a question asked: What is the probability that in a group of teachers we randomly select either an Italian or a male. [Basically a teacher can be an Italian and a male at the same time(ex.Mr.D'Onofrio), so it is said that these two events are non-mutually exclusive. We subtract the intersection of A and B to get rid of any duplicates.]

The following table illustrates the distribution of elementary and secondary school enrolment in public and private institutions in Canada in 1977.

Province/Territory	Public	Private
CANADA	5,285,274	185,035
Newfoundland	157,803	293
PEI	27,919	-
Nova Scotia	201,759	1,410
New Brunswick	163,317	393
Quebec	1,319,511	86,110
Ontario	1,974,266	58,226
Manitoba	225,854	7,642
Saskatchewan	219,327	1,573
Alberta	441,255	6,070
British Columbia	536,481	23,318
Yukon	4,866	-
NWT	12,916	-

If a Canadian student was selected at random, what would be the probability that the student was:
(a) from Ontario?

(b) from either Ontario or Quebec?


(c) from the public system?


(d) from either Ontario or the Private system?


(e) from either Manitoba or the Yukon?
Refer to (b)
Ans = 0.044