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I'm trying to represent conditional probability using a Venn diagram. I think the appropiate representation of $P(A|B)$ would be, referring to this image: http://maggiecakes.files.wordpress.com/2012/06/venn-diagram.jpg

to take the $A$ & $B$ section but "discard" the "$A$ and not $B$" part form the image, so the total possible values are just the ones contained on $A$.

Does this make any sense?

Given that this reasoning is right (and hejseb answer says it is) how can we understand Bayes Theorem under in this image? My take is that, in the Theorem formula $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$ the $P(B|A)P(A)$ represents just the "A and B" section, and it is normalized by the total area, which is the B section; this would be coherent with the first part of the question. Is that right?

TooTone
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carllacan
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    Possible duplicate. There is a post by me about representing Bayes Theorem using a Venn diagram: http://math.stackexchange.com/questions/610448/conditional-probability-intuition/610461#610461 – rookie Feb 19 '14 at 14:10
  • Yes, you are right, my question didn't involve Bayes Theorem at all. I think however that it would be interesting to extend it to Bayes Theorem. – carllacan Feb 19 '14 at 14:33
  • I just did and it is perfect. For everyone interested on my question that article is the perfect answer. However the question on which it was originally posted is not the same as one, so I don't think mine should be considered duplicate. – carllacan Feb 19 '14 at 14:52

2 Answers2

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You are almost there. $P(A|B)$ is the size of $A$ & $B$ relative to the size of $B$. So the part you discard, so to speak, is the "$A$ and not $B$" part.

hejseb
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  • Ah, right, I actually mistiped. The reason I thought of this is that in $P(A|B)$ we take that B is true, so we are only interested on the "sub-diagram" on which B is true, that is the B circle. Is that right? – carllacan Feb 19 '14 at 14:30
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Though hejseb and TooTone answers are very valuable I think the best answer is the blog post mentioned by gjdanis in this comment

I add it here as an answer for completeness: http://oscarbonilla.com/2009/05/visualizing-bayes-theorem

Community
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carllacan
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