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Dependent events

Hi
Can someone please give an example of dependent events and also tell me if they can be represented on Venn diagrams like independent and mutually exclusive events?
Reply 1
Original post by Absurd_
Hi
Can someone please give an example of dependent events and also tell me if they can be represented on Venn diagrams like independent and mutually exclusive events?

There are lots of examples (maybe google it?) such as drawing balls from a bag without replacement
https://www.google.com/search?q=dependent+examples+probability
and the conditional test is its not independent so p(B|A) != p(B).

So if you can interpret independent on a venn diagram then being dependent is not independent. However, apart from some simple cases, being able to spot dependent/independent on a venn diagram isnt necessarily obvious.

Do you have an example / question / ... youre working on?
Reply 2
Thank you , Im not working on a question at the moment but I am still confused on whether or not you can represent dependent events on a venn diagram
Reply 3
Original post by absurd_
Thank you , Im not working on a question at the moment but I am still confused on whether or not you can represent dependent events on a venn diagram

Tbh, not very clearly. In special cases its clear, but more generally dependent/independent its always easy to determine from a venn diagram. If you use the independence definition
p(A&B) = p(A)*p(B)
can you really say whether or not the probability/area fraction of the overlap is the product of the probability/area fraction of the two circles? If they dont overlap or completely overlap or close to those extremes then you can pretty much infer dependent, but otherwise its a quantitative test.
https://www.youtube.com/watch?app=desktop&v=hfQuIqAF4TE&ab_channel=Solve4x
(edited 1 month ago)
Reply 4
Original post by mqb2766
Tbh, not very clearly. In special cases its clear, but more generally dependent/independent its always easy to determine from a venn diagram. If you use the independence definition
p(A&B) = p(A)*p(B)
can you really say whether or not the probability/area fraction of the overlap is the product of the probability/area fraction of the two circles? If they dont overlap or completely overlap or close to those extremes then you can pretty much infer dependent, but otherwise its a quantitative test.


Oh I think i get it now , tysm
Reply 5
Original post by mqb2766
Tbh, not very clearly. In special cases its clear, but more generally dependent/independent its always easy to determine from a venn diagram. If you use the independence definition
p(A&B) = p(A)*p(B)
can you really say whether or not the probability/area fraction of the overlap is the product of the probability/area fraction of the two circles? If they dont overlap or completely overlap or close to those extremes then you can pretty much infer dependent, but otherwise its a quantitative test.
https://www.youtube.com/watch?app=desktop&v=hfQuIqAF4TE&ab_channel=Solve4x


So you know formula right?
[ P(A or B) = P(A)+P(B) - P(A and B) ]
Do you use this for dependent or independent events?
Reply 6
Original post by Absurd_
So you know formula right?
[ P(A or B) = P(A)+P(B) - P(A and B) ]
Do you use this for dependent or independent events?

The addition formula is general formula so works for both. The only difference is how you get p(AnB) as above. If its p(A)*p(B) then independent, otherwise its dependent.
Reply 7
Thank you for the help
Reply 8
Original post by mqb2766
The addition formula is general formula so works for both. The only difference is how you get p(AnB) as above. If its p(A)*p(B) then independent, otherwise its dependent.


Im really sorry but can you help me with this as well please
Does this formula P(B and A) = P(B|A) *P(A) only work for dependent events?
Reply 9
Original post by Absurd_
Im really sorry but can you help me with this as well please
Does this formula P(B and A) = P(B|A) *P(A) only work for dependent events?

No, thats a general formula. For inddependent events p(B|A)=p(B) so
p(AnB) = p(B|A)p(A) = p(B)p(A)

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