# Mutually exclusive/independent events

• Nylex
In summary, the difference between mutually exclusive events and independent events is that mutually exclusive events cannot both happen at the same time, while independent events do not have any effect on each other's probability. Mutually exclusive events are contrasted with non-mutually-exclusive events, while independent events are contrasted with dependent events.
Nylex
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?

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?
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 .

## What is the difference between mutually exclusive and independent events?

Mutually exclusive events are events that cannot occur at the same time. This means that if one event happens, the other event cannot happen. On the other hand, independent events are events that have no influence on each other. The outcome of one event does not affect the outcome of the other event.

## How can I identify if two events are mutually exclusive or independent?

To identify if two events are mutually exclusive, you can ask yourself if the occurrence of one event would make the other event impossible. If the answer is yes, then the events are mutually exclusive. To determine if two events are independent, you can ask if the outcome of one event has any impact on the outcome of the other event. If the answer is no, then the events are independent.

## Can two events be both mutually exclusive and independent?

No, two events cannot be both mutually exclusive and independent. If two events are mutually exclusive, it means that they cannot occur at the same time, and therefore cannot be independent.

## What is the formula for calculating the probability of mutually exclusive events?

The formula for calculating the probability of mutually exclusive events is P(A or B) = P(A) + P(B), where P(A) and P(B) are the probabilities of event A and event B, respectively.

## Can two events be dependent and mutually exclusive at the same time?

No, two events cannot be dependent and mutually exclusive at the same time. If two events are mutually exclusive, it means that the occurrence of one event makes the other impossible, which is the opposite of being dependent.

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