Mutually exclusive/independent events

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Discussion Overview

The discussion centers on the distinction between mutually exclusive and independent events, exploring their definitions and implications in probability theory. Participants seek clarification on these concepts without delving into mathematical formulations.

Discussion Character

  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant asks for a verbal explanation of the difference between mutually exclusive and independent events.
  • Another participant provides examples, stating that in a single coin flip, heads and tails are mutually exclusive, while in two flips, the outcomes are independent.
  • A further elaboration explains that mutually exclusive events cannot occur simultaneously, while independent events do not influence each other.
  • Examples involving drawing cards from a deck illustrate that drawing an ace and a king are mutually exclusive, while drawing an ace and a spade are not. The discussion also covers how the dependency of events changes based on whether a card is returned to the deck.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of mutually exclusive and independent events, but the discussion remains exploratory, with no formal consensus on all nuances presented.

Contextual Notes

Some participants suggest considering non-mutually-exclusive and dependent events for a fuller understanding, indicating that the discussion may not cover all aspects of the topic.

Nylex
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Can someone please explain to me what the difference is between these two terms (in words, not maths)?

If A and B are mutually exclusive events, then A and B can't both happen at the same time. Is that right? What's the difference between that and if A and B were independent? :confused:
 
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Coin flip example:

One flip: Heads or Tails are mutually exclusive events

Two flips: The outcome of each flip is independent.
 
That sort of makes sense, thanks.
 
Nylex said:
If A and B are mutually exclusive events, then A and B can't both happen at the same time. Is that right?
Right.
What's the difference between that and if A and B were independent? :confused:
For starters, there is a link between mutually exclusive events- they can't both happen at once. However, there is no link between independent events- they don't effect each other at all. It might be easier to understand if you also consider non-mutually-exclusive events and dependent events.
If I draw one card from a deck, drawing an ace and drawing a king are mutually exclusive events- a single card cannot be both an ace and a king. However, drawing an ace and drawing a spade are not mutually exclusive events- a single card can be both an ace and a spade.
If I draw one card, return that card to the deck, and then draw another card, the draws are independent of each other- the sample space is the same for both draws because I returned the first card to the deck. If I draw one card, but do not return that card to the deck, and then draw another card, these events are dependent- the sample space is different since I didn't return the first card to the deck. Say I drew an ace the first time. Then there is one less card and one less ace in the deck, so the probabilities for the second draw have changed.
So mutually exclusive events are contrasted with non-mutually-exclusive events, asking whether one event excludes the other. Independent events are contrasted with dependent events, asking whether one event effects the probability of the other.
 
Thanks, honestrosewater, that's also good :smile:.
 

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