Formulas for three-component set problems

Thanks for the info, but I dont believe point 6 makes much sense...


No of persons in at least one set : P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC) = A+B+C+X+Y+Z+2O


So you're saying its > P(AUBUC)???

Please feel free to contradict or add any missing pieces....

I will let the OP address the question regarding point #6 above, which I suspect may be an innocent typo. But let me put in a very enthusiastic plug for the method which follows the all-caps line in that original post referring to the diagram.

I have found, almost without exception, that what has worked for many of my students (sometimes after a bit of arm-twisting) is to assign DIFFERENT variables to the total numbers of people within groups [here expressed as "P(A)" etc] and to each segment of the venn diagram.

For example, let's pretend we are doing a two-set overlap counting students taking Physics and Biology courses. We'll call the total number of students taking physics P, the total taking biology B, and assign additional variables as follows:

w = number taking ONLY physics
y = number taking ONLY bio
x = number taking BOTH (this is the football-shaped overlap of the venn diagram)
z = number taking NEITHER.

So, using those variables, we can express any total that we need:

P = w + x
B = y + x
PuB: x + y + z
PnB: x

And so on ...

Again, nothing WRONG with assigning only one set of variables and subtracting the overlaps, but I've found that the all-addition method tends to reduce unforced errors significantly. Just one instructor's two cents!

And yes, many thanks to amitdgr for the original post!

Cheers, Steve P.

its X+Y+Z+A+B+C+O I THINK