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What is the difference between independent and mutually exclusive events?

Two events are mutually exclusive if they can't both happen.

Independent events are events where finding out about one doesn't change the probability of the other.

Are these definitions correct? Wha t should be its example and counter exa mple, its great if you can give

more than one.

(probability)

edited Oct 3 at 16:03

nbro

1,547 5 20

asked Sep 22 '14 at 5:24

Adnan Ali

186 1 1 8

6 Answers

Yes, that's fine.

Events are mutually exclusive if the occurrence of one event excludes the occurrence of the

other(s). Mutually exclusive events cannot happen at the same time. For example: when

tossing a coin, the result can either be or but cannot be both.heads tails

m u t u a l l y e x c l u s i v e A , B

P ( A B )

P(

A

B)

P ( A B )

P ( A B )

= 0

=P

(A ) + P ( B )

= 0

=

P ( A )

1 P ( B )

Events are independent if the occurrence of one event does not influence (and is not

influenced by) the occurrence of the other(s). For example: when tossing two coins, the result

of one flip does not affect the result of the other.

i n d e p e n d e n t A , B

P(

A

B)

P ( A B )

P ( A B )

P(

A B )

=P

(A

)P

(B

)

= P ( A ) + P ( B ) P ( A ) P ( B )

= P ( A )

=P

(A

)

This of course means mutually exclusive events are not independent, and independent events

cannot be mutually exclusive. (Events of measure zero excepted.)

edited Sep 22 '14 at 10:27 answered Sep 22 '14 at 5:46

Graham Kemp

29k 2 10 35

can i get a real life example for better understanding. take a look i have edited Question and made it moreclear. Adnan Ali S ep 22 '14 at 5:48

1 "This of course means..." Events of probability zero excluded. Did Sep 22 '14 at 6:21

Is there any connection between independent events and mutually exclusive events? I meant to ask "If

and

A

are mutually exclusive, what can be commented on the independence ofB andA or vice versa."

Or is there no such connection at all? I guess there is none. But just want to confirm.

B

Mahesha999May

23 at 15:22

3 @Mahesha999 If two events are mutually exclusive, then they are NOT independent. PramodJun 24 at

1:11

If I toss a coin twice, the result of the first toss and the second toss are independent.

However the event that you get two heads is mutually exclusive to the event that you
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get two tails.

Suppose two events have a non-zero chance of occurring.

Then if two the events are mutually exclusive, they can not be independent.

If two events are independent, they cannot be mutually exclusive.

edited Sep 22 '14 at 6:01 answered Sep 22 '14 at 5:52

copper.hat

83.1k 4 35 106

:- two event are mutually exclusive event which they can not

occur at the same time . e.g if we flip a coin so there will be only on possibilities of out comes

that may be tail or head.

Mutually exclusive event

:- the occurrence of one event dose not effect the occurrence of the

others e.g if we flip a coin tow times at the first time may be head will come , but next time

when we will flip the coin ag ain the out come will become head so from this example we can

see the first event dose not effect the occurance of the next event

Independent event

edited Jan 22 at 5:10

aksam

143 7

answered Jan 12 at 20:11

Obaidullah Habibi

31 1

After reading the answers above I still could not understand clearly the d ifference between

mutually exclusive AND independent events. I found a nice answer by Dr. Pete posted on

. So I attach it here so that op and many other confused guys like me could save some of

their time.

math

forum

a real-life example is the following. Consider a

fair coin and a fair six-sided die. Let event A be obtaining heads, and event B be rolling a 6.

Then we can reasonably assume that events A and B are independent, because the outcome

of one does not affect the outcome of the other. The probability that both A and B occur is

If two events A and B are independent

P(A and B) = P(A)P(B) = (1/2)(1/6) = 1/12.

is the following. Consider a fair six-sided

die as before, only in addition to the numbers 1 through 6 on each face, we have the

property that the even-numbered faces are colored red, and the odd-numbered faces arecolored green. Let event A be rolling a green face, and event B be rolling a 6. Then

An example of a mutually e xclusive event

P(A) = 1/2 P(B) = 1/6

as in our previous example. But it is obvious that events A and B cannot simultaneously

occur, since rolling a 6 means the face is red, and rolling a green face means the number

showing is odd. Therefore

P(A and B) = 0.

Therefore, we see that a mutually exclusive pair of nontrivial events are also necessarily

dependent events. This makes sense because if A and B are mutually exclusive, then if A

occurs, then B cannot also occur and vice versa. This stands in contrast to saying the

outcome of A does not affect the outcome of B, which is independence of events.

answered Feb 1 at 17:17

minerals

132 5

Think simple,for independents events we have two events (two different events like tossing coin

and rolling a disc,tossing two coins).So,probability of occurence of one does not effect the

probability of occurence of other.In case of mutually exclusive events we have also two

evevts(may be more than two) but difference is that the events are derived from the same

events (rolling dices with even number red coloured and odd number green coloured.here both

events have from the only single dice not for two).

answered Aug 21 at 17:54
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sachin kumar

1

Events are Independent when happening of one does not influence happening of other.

Eruption of volcano on Earth and orbit of Mars do not influence each other, so are

independent events.

Growth of human population and preservation of many other species are mutually exclusive,

as the one can only happen if the other does not happen.

Strictly speaking, mutually exclusive does not imply that one of them must happen. If there is alarge asteroid impact on Earth, then neither human population grows nor endangered species

are p reserved.

answered May 21 at 19:30

akhil999in

1

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