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Trying to do an execise where I have given this table

enter image description here

Find out

A 1000 Ohm resistor that is selected came from Bin number 4

I then tried drawing a venn diagram, but it seems wrong enter image description here

If these are the right values I put in the venn diagram, how do I find the intersection between them so I can answer this question

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    shouldn't it be 1000 instead of 1200?2012-11-05

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Intersection is both A and B, ie $A\cap B$ so it should be the amount in the overlap, ie 600.

That table is setup like this:

\begin{array}{l c l c l c l } & A_1 & A_2 \\ B_1 & A_1 \cap B_1 & A_2 \cap B_1 & \mbox{total of }B_1 \\ B_2 & A_1 \cap B_1 & A_2 \cap B_2 & \mbox{total of }B_2 \\ & \mbox{total of }A_1 & \mbox{total of }A_2 & \mbox{total of }S \end{array}

Where the set A is split into 2 disjoint parts, wlog B is as well S is the total set (sample space)

What you need is Bayes' Theorem

P(1000 Ohms | Bin 4) for ease of typing O = 1000 Ohms , B = Bin 4

$P\left(O|B\right) = \frac{P\left(B|O\right)P\left(B\right)}{P\left(B|O\right)P\left(O\right) + P\left(B|\bar{O}\right)P\left(\bar{O}\right)}$

$P(not a)= P\left(\bar{a}\right) = 1- P(a)$