Amirfunc wrote:

Jabjagotabhisavera why are we not using the other formula, shouldn't we use this formula Total= A+B+C -(sum of 2 group overlaps)+ (All three) + Neither

Though the answer will still be 'E'

Hi Amirfunc,

We can use any formula we wish, but we need to understand the the meaning of the the term we are using and also need to understand how the formula is derived basically.

Attachment:

Statistics.jpg [ 30.03 KiB | Viewed 513 times ]
Refer to the figure above, we can say that.

Total = a+b+c+d+e+f+g+Neither (N) ------------------------------------------------------Equation 1

The question is asking us to find out the value of exactly 2 group overlapping, so basically the value of d+e+f.

So, sum of exactly 2 groups overlapping is d+e+f ------------------------------------------Equation 2

Notice that A=a+d+g+f => a = A-d-g-f -----------------------------------------------------Equation 3

Similarly B=b+d+g+e => b = B-d-g-e -----------------------------------------------------Equation 4

and C=c+e+g+f => c = C-e-g-f --------------------------------------------------------------Equation 5

Putting the value of equation 2,3 and 4 in equation 1, we get

Total = (A-d-g-f) + (B-d-g-e) + (C-e-g-f) +d +e + f + g + N = A+B+C -2*(d+e+f)+(d+e+f) - 2*g +N = A+B+C -(d+e+f) - 2*g +N

Using the definition from equation 2 in the above formula, we can say

Total = A+B+C -(d+e+f) - 2*g +N -----------------------------------------------------------Equation 6

Total = A+B+C -(Sum of exactly 2 groups overlapping) - 2*intersection of all three +N ------------Equation 7

Now coming back to the formula you refer to, first we need to understand what is the meaning of different terms used here.

Total= A+B+C -(sum of 2 group overlaps)+ (All three) + Neither ---------------------Equation 7

sum of 2 group overlaps = A∩B + B∩C + C∩A = d+g + e+g + f+g

Using the formula from Equation 6

Total = A+B+C -(d+e+f) - 2*g +N

Add and subtract 3*g in the above equation, we get

Total = A+B+C -(d+e+f) - 2*g +N +3*g -3*g = A+B+C -(d+e+f + 3*g) - 2*g +3*g +N = A+B+C -([d+g]+ [e+g]+ [f+g]) - g +N = A+B+C -(A∩B + B∩C + C∩A) - A∩B∩C +N

Total = A+B+C -(A∩B + B∩C + C∩A) + A∩B∩C +N

Total = A+B+C -(sum of 2 group overlaps) + intersection of all three +N

So, summery is

1. Formula I used and the formula you refer to can be derived using the basic concept as long as we are a using the correct meaning of the different terms used here.

i. sum of 2 group overlaps = A∩B + B∩C + C∩A = d+g + e+g + f+g

ii. Sum of exactly 2 groups overlapping = d+e+f

Hope, I was able to explain how both the formula are derived from the basic concept and why I used a particular formula [As question is asking about the value of "Sum of exactly 2 groups overlapping"] to solve this question.

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