# Mutually exclusive and exclusive

#### denian

currently, im studying probability in my school.

i'm bit confused with the difference btw :-
(a) mutually exclusive and exclusive
(b) independent and mutually exclusive.

anyone can explain?

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#### mathman

(a) I'm not sure what you are trying to describe.
(b) Mutually exclusive - the probability that both will happen is 0.
Independent - probability that both will happen is the product of the probabilities of the individual events.

#### HallsofIvy

Homework Helper
I'm with mathedman. I have never heard the term "exclusive" used in probability except as part of "mutually exclusive". I would be inclined to say that "exclusive" and "mutually exclusive" are the same thing.

As mathedman said: if two events are "mutually exclusive" then the probability of both happening is 0 (P(A and B)= 0). If they are independent, P(A and B)= P(A)*P(B).

#### hypnagogue

Staff Emeritus
Gold Member
Or, in linguistic terms:

If two events are mutually exclusive, then it is impossible for both to happen-- the occurence of one necessarily excludes any chance that the other occurs.

If two events are independent, then they do not influence eachother-- the occurence of one does not change the probability that the other will happen.

For instance, let
A: the event that I leave my house to go to my 9-5 job today
B: the event that I sleep in my house until 5pm today
C: the event that someone calls my home phone number
D: the event that a coin flip comes up heads

A and B are mutually exclusive events, since if I sleep until 5pm I can't go to work that day, and likewise if I go to work then I must have been awake before 5pm. A and C are not mutually exclusive, since going to work does not exclude the possibility that someone places a call to my home phone, and vice versa.

A and D are independent events, since my going to work does not affect the chance that a coin flip comes up heads, and vice versa (assuming I'm not fatalistic enough to base my decisions on a coin toss, of course). However, B and C are not independent events, since if I sleep until 5pm, my sleepiness affects a greater chance that someone (my overly demanding employer, for one ) will call my house to see what's going on.

Actually, it is useful to think of mutual exclusion and independence as exact opposite relations. If two events X and Y are independent, then knowing that X occurs gives you absolutely no relevant information as to the probability of Y occuring. On the other hand, if X and Y are mutually exclusive, then knowing that X occurs gives you complete information as to the probability of Y occuring, since you know that there is no chance that Y can occur.

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