My Math Forum Confused About Mutual Exclusivity with More Than Two Events

 Probability and Statistics Basic Probability and Statistics Math Forum

October 6th, 2019, 02:34 AM   #11
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Quote:
 Originally Posted by skipjack Three or more events are called mutually exclusive, or disjoint if each pair of events is mutually exclusive. That's the exact wording from a textbook. Have you found another textbook that disagrees with that?
I agree with the definition:

Events are mutually exclusive if any of them discards the rest. (it is a simplified definition.)

$E_1$ discards the $E_2 \; \& \; E_3$. So M.E....

Give me a reference for your definition.

October 6th, 2019, 06:55 AM   #12
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Quote:
 Originally Posted by tahirimanov19 I agree with the definition: Events are mutually exclusive if any of them discards the rest. (it is a simplified definition.) $E_1$ discards the $E_2 \; \& \; E_3$. So M.E.... Give me a reference for your definition.
Well, I am confused again!

tahirimanov19 and skipjack seem to currently disagree on the correct (or most commonly used) definition of mutual exclusivity. When in the context of more than two events, each definition produces different results.

The three events are not mutually exclusive if the definition is:
A set of events are mutually exclusive if all pairs of events within the set are mutually exclusive.

skipjack seems to subscribe to this definition.

The three events are mutually exclusive if the definition is:
A set of events are mutually exclusive if at least one pair of events within the set are mutually exclusive.

tahirimanov19 seems to subscribe to this definition.

I mean, I suppose each definition is correct if speaking within a specific context, but which one of these definitions would you guys say is more widely accepted in general?

Thanks a lot to both of you for providing help!

October 6th, 2019, 07:26 AM   #13
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Quote:
 Originally Posted by skipjack Three or more events are called mutually exclusive, or disjoint, if each pair of events is mutually exclusive.
As a layperson, this is the definition I would have guessed. As someone accustomed to interdisciplinary audiences, this sounds like the type of thing you would want to define early on in your talk to avoid confusion.

October 7th, 2019, 05:49 AM   #14
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 Originally Posted by DarnItJimImAnEngineer As a layperson, this is the definition I would have guessed. As someone accustomed to interdisciplinary audiences, this sounds like the type of thing you would want to define early on in your talk to avoid confusion.
What is your view on mutually inclusive events?

October 7th, 2019, 07:11 AM   #15
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Quote:
 Originally Posted by Spud What is your view on mutually inclusive events?
I have never heard the term before, but if I had to hazard a guess, it sounds like mutually inclusive events would be either identical or logically linked, such that
$A$ and $B$ are mutually inclusive $iff ~ A \leftrightarrow B$.
E.g., [I roll an even number], [I roll one greater than an odd number]
or, [I post a public video to YouTube], [People post racist comments on my video]
One can't happen without the other.

October 7th, 2019, 07:45 AM   #16
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Quote:
 Originally Posted by DarnItJimImAnEngineer I have never heard the term before, but if I had to hazard a guess, it sounds like mutually inclusive events would be either identical or logically linked, such that $A$ and $B$ are mutually inclusive $iff ~ A \leftrightarrow B$. E.g., [I roll an even number], [I roll one greater than an odd number] or, [I post a public video to YouTube], [People post racist comments on my video] One can't happen without the other.
Hmm, interesting.

I was thinking more along the lines of:
Two events are mutually inclusive if they can occur at the same time.

But you seem to be saying must, instead of can.

Which, of course, is fine. I'm just wondering what people think of the term mutually inclusive because I'm not really sure.

When rolling a die, I would say Roll a 4 and Roll an Even Number are mutually inclusive events because they can occur together, even though it's possible that they don't occur together (or at all).

 October 7th, 2019, 08:06 AM #17 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2271 Google: No results found for "Events are mutually exclusive if any of them discards the rest". Feel free to do a Google search for the definition I gave.
 October 7th, 2019, 08:40 AM #18 Senior Member   Joined: Jun 2019 From: USA Posts: 310 Thanks: 162 I googled mutually inclusive, and some sources defined it as $A \cap B \ne \emptyset$ (i.e., mutually inclusive defined as not mutually exclusive, thus A and B may be independent), while other sources defined it as $(A \subseteq B) \wedge (B \subseteq A)$ (i.e., mutually inclusive means one implies the other, thus A and B are not independent). I would probably add the, "We are defining mutually exclusive/inclusive to mean...," disclaimer to any talk, paper, or discussion on the subject to avoid confusion.
October 7th, 2019, 11:27 AM   #19
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Quote:
 Originally Posted by DarnItJimImAnEngineer I would probably add the, "We are defining mutually exclusive/inclusive to mean...," disclaimer to any talk, paper, or discussion on the subject to avoid confusion.
I completely agree. Thanks a lot for your help!

 Tags confused, events, exclusivity, mutual

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