My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 6th, 2019, 02:34 AM   #11
Senior Member
 
Joined: Mar 2015
From: Universe 2.71828i3.14159

Posts: 132
Thanks: 49

Math Focus: Area of Circle
Quote:
Originally Posted by skipjack View Post
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.
tahirimanov19 is offline  
 
October 6th, 2019, 06:55 AM   #12
Newbie
 
Joined: Aug 2018
From: Finland

Posts: 9
Thanks: 0

Quote:
Originally Posted by tahirimanov19 View Post
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!
Spud is offline  
October 6th, 2019, 07:26 AM   #13
Senior Member
 
Joined: Jun 2019
From: USA

Posts: 310
Thanks: 162

Quote:
Originally Posted by skipjack View Post
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.
DarnItJimImAnEngineer is offline  
October 7th, 2019, 05:49 AM   #14
Newbie
 
Joined: Aug 2018
From: Finland

Posts: 9
Thanks: 0

Quote:
Originally Posted by DarnItJimImAnEngineer View Post
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?
Spud is offline  
October 7th, 2019, 07:11 AM   #15
Senior Member
 
Joined: Jun 2019
From: USA

Posts: 310
Thanks: 162

Quote:
Originally Posted by Spud View Post
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.
DarnItJimImAnEngineer is offline  
October 7th, 2019, 07:45 AM   #16
Newbie
 
Joined: Aug 2018
From: Finland

Posts: 9
Thanks: 0

Quote:
Originally Posted by DarnItJimImAnEngineer View Post
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).
Spud is offline  
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.
skipjack is offline  
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.
DarnItJimImAnEngineer is offline  
October 7th, 2019, 11:27 AM   #19
Newbie
 
Joined: Aug 2018
From: Finland

Posts: 9
Thanks: 0

Quote:
Originally Posted by DarnItJimImAnEngineer View Post
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!
Spud is offline  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
confused, events, exclusivity, mutual



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Probability of Events, Simultaneously or One by One Events palongze Probability and Statistics 8 January 5th, 2017 06:39 PM
Mutual fund investment shunya Elementary Math 1 December 10th, 2015 04:21 PM
Computing Mutual Information in Bayesian network thesamad@gmail.com Advanced Statistics 1 August 10th, 2012 05:19 AM
How can I compare the following mutual information values ? aneuryzma Advanced Statistics 0 June 13th, 2011 12:08 AM
Maximization of the sum of mutual information terms miggimig Applied Math 0 August 10th, 2009 05:28 AM





Copyright © 2019 My Math Forum. All rights reserved.