Geometry....

J

jenzy569

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Jul 13, 2009
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Consider the Venn diagram below. The numbers in the regions of the circle indicate the number of items that belong to that region.

(2 intersecting circles A & B, where A part is 50, B part is 110, and the intersecting part is 40)

Determine:

n(A)
n(B)
P(A)
P(B)
P(A|B)
P(B|A)
 
You can't do even one? Come on!! Did you attend class? Do you have a book?
 
well B part is 110 and all the parts added together is 200....did i do it wrong??
 
First, please stop assuming it is wrong. Do your best to gain a little confidence.

Second, if you add up all there is, that is, indeed, the total. You did that. Why do you doubt?

Why not start with the simplest questions? Do you know what n(A) means? Answer that next. You seem to have figured out n(B). Good work on that. What is n(A)?
 
because i wasn't sure if that was how you do it, seemed a little too easy haha....is n(a) 150/200??
 
No, what's the difference between n(A) and P(A)?

You are given
n(A Alone (without B)) = 50
n(B Alone (without A)) = 110
n(A and B) = 40

This gives

n(A) = 50 + 40 = 90
n(B) = 110 + 40 = 150

We already have

n(entire universe) = 50 + 110 + 40 = 200

Okay, now we are ready for P(A) and P(B). What say you?
 
P(A) means chance of A happening (with or without B)
 
jenzy569 said:
oh okay....i thought n(A) meant not A....yes we shall continue....
Click to expand...

Oh dear. Does it? I thought n(A) was the number of elements or the size of A. Do you have a carefully written definition?

My friends at Minnesote State seem to agree with my definition.

http://www.mnstate.edu/peil/MDEV102/U1/S2/S2.pdf

No worries. It's important to get the notation down. Now you know.
 
jenzy569 said:
so P(A) = 50 and P(B) = 110 ??
Click to expand...
No, probabilities always lie between 0 and 1.
n(A) means the number of elements in the set A. It can range from 0 on up to infinity.
n(B) means the number of elements in the set B.

n(A) = n(A excluding B) + n(A including B) = 50 + 40 = 90.
So, what is n(B)?
What is n(the union of A and B)?

If the assumption is made that the union of A and B forms the relevant universe and that each element of that universe has an equal probability, THEN
P(A) = n(A)/n(union of A and B) BY DEFINITION
So what Is P(A)?
What is P(B)?
What is P(the intersection of A and B)?
What is the definition of P(A | B)?
What is the definition of P(B | A)?
 
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