Are mutually exclusive events independent?
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- Опубликовано: 20 янв 2018
- Are mutually exclusive events independent? I get asked variants of this question frequently, so it’s evident that some students confuse these two concepts. The one sentence summary: If A and B are mutually exclusive events, then they are independent if and only if P(A) = 0 or P(B) = 0. I take a more detailed look in this video.
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Very clear, that's the conclusion I had looking at the mutually exclusive A & B, only dependence between A & B can explain why (A and B) is 0
I have been puzzled by this point for a long time. You explain this concept really clearly. I am grateful for your explanation!
Thank you so much! I have a test on this material tomorrow, and now I will not fail! :)
Thank u so much sir for ur wonderful explanation. I have asked the same question to many others who couldn't answer my question satisfactorily bit it is u who explained my doubt the way I wanted.
Thank you for the explanation! You explain it very clearly!
upload as much as you can about this topic, I'm a cs student and your vids really helps. :) thanks
Glad to see you back
Thanks!
Hi hamza
Best video ever
Amazing explanation. Thank you!
the best teacher ever. thnkyou so much
Exactly what i was searching for
Thanks alot
Thank you. Finally I understand this
So very good. No literature I know addresses this issue.
Best statistics channel !
👌Thank you for all of these videos, really!
You are very welcome!
Excellent job!
best teacher on earth
Mind blowing explanation
check if you could add some numerical examples in your videos too.
Great concept!
thank you very much for this!
Excellent explanation
Thanks! I could write something on my test! I am super thankful 🥳
Tanisha Upadhyay Tanisha hey! Mutually exclusive events are entirely different than independent events
Tanisha Upadhyay Tanisha 🙃
Nicely explained ..👍
Thanks!
Suppose 2 buses cross some point between 7:00 am and 8:00 am bus A crosses after every 7 minutes and bus B crosses every 11 minutes, are both events mutually exclusive and independent?
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Life saver🎉😮
nice video... thanks
A: first die lands 1
B: second die shows larger number than first die
The answer states that P(B|A) = 5/6 and P(B) = 15/36 (by considering all combinations)
so A and B are dependent which seems to make sense.
However, A and B seem like mutually exclusive events to me as you can’t have 1 AND a number bigger than 1 at the same time. So shouldn’t P(B|A) = 0? Even tho the previous answer 5/6 seems to make more sense intuitively.
Also wouldn’t the formula P(B│A) = P(A ∩ B)/ P(A) stop working too as the numerator will now be 0 as they can’t happen at the same time? Thank you in advance.
@@jillian9098 "A and B seem like mutually exclusive events to me as you can’t have 1 AND a number bigger than 1 at the same time". You can't have the first die showing a one, and the second die showing a number greater than 1? These events are referring to different dice, or different die rolls, so they can both occur on the same trial (rolling a pair of dice).
@@jbstatistics Yes, that makes a lot of sense logically. What confuses me is when I put the values into the formula P(B│A) = P(A ∩ B)/ P(A). Supposedly it should be P(B│A) = P(A ∩ B)/ 1/6. But what would P(A ∩ B) be? As even though they CAN happen together logically, they don’t seem to intersect on a Venn diagram with 1 being in the A circle and 2,3,4,5,6 being in the B circle, which is why I thought P(A ∩ B) is 0. Could you explain this to me? Thank you so much.
When you dont understand never go to comment section
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This is probably a big philosophical question, but does this imply that mutually exclusive events are in some sense causally related?
how is that a philosophical question?
It's like if your parents say, "You can have a cat or a dog but not both". By picking a dog (The right choice), you know you won't be getting a cat. So the probability of getting a cat depends on getting a dog.
Those are some dumb ass parents for not allowing getting both. They shouldn't have children in the first place.
Thanks for that example! It gave me a good chuckle and helped me understand the concept better.
@@mrigayu Thanks! Glad to help with concepts.
Sir if you are reading this please help ok?when two separate events or trials are happeng say roll a dice and flip a coin,flipping coins and rolling dice have different sample spaces.What does and actually mean in this case?That region if intersection in venn diagram although they dont share the same sample spaces?And also is the and concept of that addition rule the same "and" we refer in multiplying probabilities or are they different?
They do share the same sample space. If we are discussing two events, and the notions of whether or not they are mutually exclusive or independent, then we are talking about two events *in the same sample space*. In your example, if we flipped a single coin and observed what side comes up, and rolled a single die and observed the number on the top face, then one way of expressing the sample space would be S ={T1,T2,T3,...,H5,H6}. Here, these 12 sample points are all equally likely (assuming a balanced die, fair coin, and that the toss and roll are independent).
The final term in the addition rule (P(A n B)) is the probability of the intersection of A and B. It is only equal to the product of the individual probabilities if A and B are independent.
@@jbstatistics wow sir you made it super clear..thanks for your time..have no words to thank you and your contents..best of luck for 1m+ subs
Basically, since the probability of their intersection DOES NOT EQUAL the product of the individual probabilities, implies that P(A) and P(B) ARE NOT INDEPENDENT.
*For dependant events they ARE EQUAL.
@@Verifyourage thank you for your help. it's interesting how time flies away so quick. I am at graduate school in math rn and asked this wayyyy earlier during my college days
Never forget your posterior; i never forgot you existed jbstats
Thanks! I kept up my end of the bargain; I kept existing.
Sir, if for the mutually exclusive events we consider A=The event of getting an odd number on a fair die and B=The event of getting an even number on a fair die, won't we get that the two events are dependent on each other when in reality they aren't?
They are dependent because if you were to get an odd number which we suppose is event B and you make it the condition for the occurence of event A (getting an even number ) then we know the conditional probability is P(A/B)=0
It is an example of how mutually exclusive events are not independent instead in all cases they are dependent (independent only when P(A)=P(B)=0 which satisfies the equation as P(A n B)=P(A)=P(B) we cannot have probability of any of the events as not equal to 0 and satisfy the P(A/B)=P(A) and P(B/A)=P(B)
3 years after
It doesn't feel like it, but that clock just keeps on ticking.
Anyone help me plz?
Mutually exclusive is always dependent because the outcome of one always influences the outcome of the other
Yes because if one of them occurs the other event cannot occur . Therefore they cannot co-occur
P(A/B) cannot occur . Similarly P(B/A) cannot occur
really nice video sir
sir any example of dependant event which is not mutually exclusive
I have a number of examples in my videos on independence. It's extremely common for two events to be not mutually exclusive and not independent. For example, consider rolling an ordinary single six-sided die once and observing the number on the top face. Let A = {1,2,3}, B = {3}, C = {3,4,5}. All 3 pairs of events are not mutually exclusive and not independent.
@@jbstatistics yes sir but it is not also dependant
right because rolling dia is an independent event
@@rishitshah4087 There is more than one problem with your statement. First, the events I give in that situation are not mutually exclusive and not independent. "Not independent" and "dependent" have exactly the same meaning. Rolling a die is an action, it is not an event. I believe you may be referring to the situation where people assume that repetitive die rolls are independent, but that has nothing to do with the example I outlined (which involved a single roll).
You just made my brain hurt a lot more.
Love your videos.
For mutually exclusive events P(A U B) = P(A) + P (B). Otherwise P(A U B) = P(A) + P(B) - P(A ∩ B)
For independent events, P(A ∩ B) = P(A).P(B)
Just to clear the first part up a bit:
It's *always* the case that P(A U B) = P(A) + P(B) - P(A ∩ B). When A and B are mutually exclusive, P(AnB) = 0 and thus P(A U B) = P(A) + P(B).
Loganathan Palanisamy /
Sir, what is the difference between MUTUALLY INCLUSIVE and INDEPENDENT EVENTS?
Actually mutually exclusive events are those events which do not occur simultaneously or do not share a common element in the sample space U whereas independent events are those whose probability of occurence remains unchanged whether they occur in the sample space or they occur on the condition that the other event has occured i.e they occur in the subset of sample space U which is the set of outcomes of the event on which it is being conditioned upon.
@@aditishikha8149 Thanks. But read the question again.
mutual inclusion is the opposite of mutual exclusion. if mutual exclusion means A ∩ B = ∅ . then mutual inclusion means the opposite, or in set theory terms, the (relative) complement.
So for mutual inclusion: A ∩ B = A which is identical to saying A ∩ B = B. All this is basically a fancy way of saying the following: If the sets A and B contain mutually inclusive events, they are the same set.
Independence: P (A ∩ B) = P(A) * P(B)
Mutual EXclusion: P (A ∩ B) = P(∅) = 0
Mutual INclusion P (A ∩ B) = P(A) = P(B)
Love you
very helpful!
man i really didnt understand anything at all could you please give an example using actual events like maybe rolling a dice and flipping a coin because i really didnt understand a single word
But how to visualise independent event using Venn diagram. I like to think that independent events belong to different sample space.
But that would make all the mutually exclusive set to be dependent except for the case in which probability of either of the event is 0.
Here's my video on what independent events look like on a Venn diagram: www.youtube.com/watch/pV3nZAsJxl0
"I like to think that independent events belong to different sample space." I don't think that's a good way to think of it at all. Events in the same sample space can be independent or dependent. Any time I'm discussing two events, I mean two events in the same sample space.
@@jbstatistics Thanks for clearing my doubt, which arose due to following thought process:
Suppose an experiment of tossing a coin and rolling a dice. Clearly the outcome of rolling dice is independent of outcome of tossing the coin.
I thought of these two action would constitute different sample space and in some sense addition of these two sample space would constitute one final sample space( H1, H2,.....H6, T1,T2,.........T6). This is how I developed the notion of separate sample space. This is exactly the same thing you did when you overlapped the two rectangle in above referred video.
Hence, independent events are different sample space of different action, and and then you combine the two sample space to get a composite sample space which follows the rule P(A intersect. B) = P(A).P(B)
@@jbstatistics for ex: A is outcome of tossing a coin. B is outcome of rolling a dice. C is the outcome of both the action.
All of the three action will have different outcome space. The outcome of A or B alone have no place in sample space of C, rather their combination form the sample space of C. Hence sample space of C is some sort of composite sample space obtained by sample space of A and B.
Independence can be defined following way:
X = the set of outcome of C formed by combining all the sample space of A (H,T) and a particular outcome of B (say 6)
If P(X)=P(B) , then we can say X is independent of A, even though A is used in composition of X, it is not affected by any choice of outcome of A
Errr........I don't know....I m kinda lost it.....this is maximum I could type on my mobile.......
@@ahmadfaraz9279 I strongly recommend that you don't think of it like this. Roll an ordinary die once. Let A = {1,2} and B = {2,4,6}. These are independent events, but one wouldn't think so if they tried to follow your line of reasoning. In your example, you're unnecessarily complicating the issue, by thinking of two sample spaces that you bring together. If they share a sample space in the end, then they share a sample space.
"Clearly the outcome of rolling dice is independent of outcome of tossing the coin." You're assuming that they are independent. Sure, from our experience in this world that's a reasonable assumption, but it's an assumption and not something that is provable mathematically. It's not a good way to think of independence, as independence can arise from a structural situations like what you describe, but also just the nature of the two events (which is at least as important to understand). Lots of resources (Khan Academy, etc.) bring up the notion of independence similar to your way, which is not a good way introduce the topic or to think about it, in my opinion. (It simply doesn't get to the heart of the meaning and can be confusing.)
only 5 minutes!
Excuse me, when A is 0, then P(A|B)=P(A and B)/P(A)=0/0=ERROR, and when B is 0, then P(A|B)=P(A and B)/P(B)=0/0=ERROR, so these are only half independent. I like your video, but I know this, and I am not much of a press-like-er.
Conditional Probability P(A|B) is only defined when P(B) not equal 0 and also in mutually exclusive disjoint events, independent probabilities of A and B are more than zeros.
You're overcomplicating things. if the Probability of an event A is 0, then the probability of A given B is also 0 because A will never happen.
Take the example: what is the probability that the results from rolling 2 six sided dice will sum to 1? Now what is the probability that the sum of 2 six sided dice will sum to 1 GIVEN the first result is a 5?