Actual difference between mutually exclusive and independent event

henry · 2008-01-15 18:18:49

What is the actual difference between mutually exclusive and independent event in term of venn diagram?
I think mutually exclusive is two separate circles in the same Venn diagram and
independent event is two Venn diagrams each consists of one circle, therefore these two circle are independent events.

henry · 2008-01-15 18:19:48

And anyone can point out my mistake?

mathsyperson · 2008-01-16 01:32:04

Maybe it'll be clearer if you look at the definitions in terms of probabilities.

I'm guessing you've been taught that the probabilities of independent events aren't affected by each other, and that mutually exclusive events can't happen at the same time.

More mathematical ways of saying those things are:

Independent: - P(A and B) = P(A)xP(B)
Mutually exclusive: - P(A and B) = 0, where A and B are two events.

Comparing those two definitions, it's clear that they're different. In fact, events can't be independent and mutually exclusive at the same time.

This is fairly clear if you think about it: If event A happens then event B can't happen, and thus event B is dependent on event A (and vice versa).

The exception to this is when one of your events is impossible, such as rolling a 7 on a dice.

Jai Ganesh · 2008-01-16 02:22:05

A coin is tossed twice. The outcome of the second is independent of the first. That is, whatever be the outcome of the first, the chance of a tail or head is exactly 50% for the second throw.

Independent is when the outcome of the first has no bearing on the second.

Mutually exclusive is when one outcome cannot be the same again. If there's one head, the other got to be a tail. The other cannot be a head too. Mutually exclusive events rule out the possibility of the same even occuring more than once.

Ricky · 2008-01-16 05:28:16

independent event is two Venn diagrams each consists of one circle

This is incorrect. There is no way to represent independent events using Venn diagrams.

Ricky · 2008-01-16 05:30:38

The confusion stems from the fact that while mutually exclusive and independent events can be used in counting techniques, only mutually exclusive(ness) can be used to describe two sets. There is not concept of two sets being independent, but rather, choosing from two sets can be independent.

Pilar · 2008-12-20 06:36:00

In using mutually exclusive events the word events can be misleading because it refers to a plural set of events happening. In reality, mutually exclusive is describing a single trial and the possible outcomes of that trial. So in flipping a single coin, the possible outcomes are two distinctive unique "events", heads or tails, and they cannot occur at the same time. Representing the possible outcomes would involve two separate sets with no intersection. Now lets look at non-mutually exclusive events. Once again it is describing the possible outcomes in a single trial. Let look at drawing a card and it being an ace of hearts. Here the possible outcome of the events are not mutually exclusive because a card can have both an ace and a heart. The venn diagram of this type of event would involve two intersecting sets.

When using independent events, the the word "events" it is truly speaking of a number of trials. In other words, you cannot independent events if only on trial has occurred. This means then that when looking at independent events, we are looking at a larger sample space because there are different possible arrangements. For instance, when rolling a single dice, there are six possible outcomes. When rolling two dice there are 36. To represent independent events, you would have to consider a new set that includes all of the 36 options. And depending on the question, the answer would be a subset of this larger set.

glenn101 · 2008-12-20 17:45:51

ok I'll put it as simple as I can.
Matually exclusive events occur if Pr(A intersect B)=null
Events A and B cannot happen at the same time. If A and B are mutually exc;isove. Pr(A intersect B)=0, so the Addition Law becomes:

Pr(A intersect B)= Pr(A)+Pr(B)
or
Pr(A or B)= Pr(A)+Pr(B)

hope that helps

Macy · 2008-12-24 12:49:14

In my opinion:
Mutual exclusive is used to describe the events in the Universal Set. Therefore we can represent our events and their relationship using Venn diagram
Independent events is used to describe two different sets or more sets. We do not use Venn diagram to describe their relationship but we use Tree Diagram.
The difference can be seen very clearly when we are talking about the conditional Probability.
With Mutual exclusive the conditional probability will be affected. Say what is the probability event A occurs if knowing B occurs?. Because A and B are in the same set therefore the outcome will be affected
Independent events at the other hand, the conditional probability will not be affected. Say What is probability event A occurs if knowing B occurs. Because they are in different sets.

MathsIsFun · 2008-12-24 15:15:12

Hi Macy and welcome to the forum ... maybe you would like to become a Member?

Macy · 2008-12-24 17:07:05

Hello MathisFun, I am the member but i am lazy to sign in. Forgive me
Merry Christmas and happy New Year

MathsIsFun · 2008-12-24 17:43:57

LOL ... Merry XMas, too

1/4s · 2009-01-23 18:14:15

Hi I was just wondering, does an event have to be either mutually exclusive or independent. I understand that they cannot be both, but can they be neither, or does an event have to be one or the other?
Thanks

mathsyperson · 2009-01-25 08:17:34

Lots of events are neither.
eg. Pick a random number between 1 and 10, and consider these two events:

A: The number is even.
B: The number is prime.

The events aren't mutually exclusive because 2 makes both happen, but they aren't independent either because a number being even makes it unlikely to be prime, and vice versa.

SeanDanahy · 2011-09-26 09:41:02

above info about the impossibility of an event being both mutually exclusive and independent is WRONG!

if the the P(A and B) = 0 AND the P(A or B) = P(A) + P(B) then the events would be both mutually exclusive and independent.

I only know this because I said no they cant be both mutually exclusive AND independent on a quiz and the STATS PhD marked it wrong with this explanation. So yes it is possible and we all make mistakes

bobbym · 2011-09-26 10:08:12

Hi SeanDanahy;

The case you point out is considered trivial and not included in the above discussion obviously. Your stats prof might have pointed that out when he took the time to point out why he marked you wrong.

Bob · 2011-09-26 11:05:02

hi SeanDanahy

Hold on a minute.

P(A and B) = 0 AND the P(A or B) = P(A) + P(B)

These are just two ways of saying the same thing. See Venn diagram

Bob

ps and in my next post I'll use a Venn diagram to illustrate independent events!

Last edited by Bob (2011-09-26 11:16:04)

Bob · 2011-09-26 11:15:23

Independent Events

Event 1 is throwing a coin and getting heads.

Event 2 is throwing a die and getting a six.

P(1 given 2) is H6/(H6 or T6) = 1 / 2 = 0.5 (note: by which I mean count up these events ... sorry, not notationally correct)

P(1 given not 2) is (H1 or H2 or H3 or H4 or H5)/(H1 or H2 or H3 or H4v or H5 or T1 or T2 or T3 or T4 or T5) = 5/10 = 0.5

Bob

Last edited by Bob (2011-09-26 11:17:53)

Math Is Fun Forum

#1 2008-01-15 18:18:49

Actual difference between mutually exclusive and independent event

#2 2008-01-15 18:19:48

Re: Actual difference between mutually exclusive and independent event

#3 2008-01-16 01:32:04

Re: Actual difference between mutually exclusive and independent event

#4 2008-01-16 02:22:05

Re: Actual difference between mutually exclusive and independent event

#5 2008-01-16 05:28:16

Re: Actual difference between mutually exclusive and independent event

#6 2008-01-16 05:30:38

Re: Actual difference between mutually exclusive and independent event

#7 2008-12-20 06:36:00

Re: Actual difference between mutually exclusive and independent event

#8 2008-12-20 17:45:51

Re: Actual difference between mutually exclusive and independent event

#9 2008-12-24 12:49:14

Re: Actual difference between mutually exclusive and independent event

#10 2008-12-24 15:15:12

Re: Actual difference between mutually exclusive and independent event

#11 2008-12-24 17:07:05

Re: Actual difference between mutually exclusive and independent event

#12 2008-12-24 17:43:57

Re: Actual difference between mutually exclusive and independent event

#13 2009-01-23 18:14:15

Re: Actual difference between mutually exclusive and independent event

#14 2009-01-25 08:17:34

Re: Actual difference between mutually exclusive and independent event

#15 2011-09-26 09:41:02

Re: Actual difference between mutually exclusive and independent event

#16 2011-09-26 10:08:12

Re: Actual difference between mutually exclusive and independent event

#17 2011-09-26 11:05:02

Re: Actual difference between mutually exclusive and independent event

#18 2011-09-26 11:15:23

Re: Actual difference between mutually exclusive and independent event

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