- #1

denian

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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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- Thread starter denian
- Start date

- #1

denian

- 160

- 0

i'm bit confused with the difference btw :-

(a) mutually exclusive and exclusive

(b) independent and mutually exclusive.

anyone can explain?

- #2

mathman

Science Advisor

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(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.

- #3

HallsofIvy

Science Advisor

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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).

- #4

hypnagogue

Staff Emeritus

Science Advisor

Gold Member

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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 each other-- 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 occurring. 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 occurring, since you know that there is no chance that Y can occur.

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 each other-- 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 occurring. On the other hand, if X and Y are mutually exclusive, then knowing that X occurs gives you

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