Understanding Conditional Probability with Venn Diagrams

So, I haven’t seen many venn diagrams which show a difference between conditional and non conditional probabilities. Also, I have seen very few venn diagrams which use straight or angled lines to divide the sets, mostly they are circles, but I’ve seen straight or angled lines used to demonstrate the concept of universal sets (see the diagram at the bottom of the post). So, I tried to make two venn diagrams showing the difference between conditional and non conditional probabilities, see the diagram above…and it seemed to make the most sense to use straight or angled lines since the sets were mutually exclusive…can someone tell me if it is correct?

Example A
Probability some is a girl 1/3, probability someone is a boy 2/3
Probability someone drives 2/5, probability someone doesn’t drive 3/5

In Example A, whether a person drives is
independent from gender, because in either
case the probability that a person (boy or girl)
drives is 3/5, and that they don’t drive is 2/5. Is that right?

Example B
Probability drive P(D): 11/15
Probability don’t drive P(DD): 4/15
Probability don’t drive qiven qirl P(DD|G): 2/5
Probabilty drive qiven qirl P(D|G): 3/5
Probability drive qiven boy P(D|B): 4/5
Probability don’t drive qiven boy P(DD|B): 1/5
Probability qirl who doesn’t drive P(G and DD): 2/15
Probability qirl who drives P(G and D): 3/15
Probability boy who drives P(B and D): 8/15
Probability boy who doesn’t drive P(B and DD): 2/15

In Example B, whether a person drives is
not independent from gender, because the probabilities
that they drive are different, conditional
depending on whether they are a girl or boy,(e.g.,
probability drive if girl=3/5, and probability girl who drives P(D|G)=3/15, whereas probability
drive if boy=4/5, and probability boy who drives is 8/15. Is this right?

Here’s another A venn diagram with angled lines, not circles, illustrating the concept of universal sets, thrown in just to illustrate that all venn diagrams do not have to be drawn with circles.

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One Response

  1. /Posting 3 years too late

    The reason universal sets use straight/angled lines is because they want to show that the information there encompasses the WHOLE of the universe. This, of course, can’t be done with circular diagrams as you’d have gaps (signalling that the set isn’t ‘universal’). That’s my understanding of it, anyway.

    Curiously enough, the first ‘venn diagram’ that you drew is actually a very good demonstration of a karnaugh map. Similarly the second one, however moreso the first. I actually find this very curious given the inter-relationship of the two types of tables. More on karnaugh maps here: http://mathsm1m0838.edublogs.org/2009/10/29/karnaugh-maps-and-probability-tables/

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