Param800 wrote:
Let me try to explain you why we are subtracting 2 * ( ABC )
So, our formula is this--
TOTAL = A + B + C - ( Sum of EXACTLY 2 group overlap)- 2*( all three) + Neither
Notice that EXACTLY (only) 2-group overlaps is not the same as 2-group overlaps:
Elements which are common only for A and B are in section d (so elements which are common ONLY for A and B refer to the elements which are in A and B but not in C);
Elements which are common only for A and C are in section e;
Elements which are common only for B and C are in section f.
Let's see how this formula is derived. Again: when we add three groups A, B, and C some sections are counted more than once. For instance: sections d, e, and f are counted twice and section g thrice. Hence we need to subtract sections d, e, and f ONCE (to count section g only once) and subtract section g TWICE (again to count section g only once).
When we subtract Sum of EXACTLY 2 group overlap from A + B + C we subtract sections d,e,and f once ( fine) and next we need to subtract ONLY section g TWICE.
For 3 set probability questions, I have developed ( or gathered ) these three basic formulas and I am able to solve any tough problem with it.
FIRST FORMULA -
TOTAL = A + B + C - ( Sum of 2 group overlap) + ( All three ) + Neither
SECOND FORMULA -
TOTAL = A + B + C - ( Sum of EXACTLY 2 group overlap)- 2*( all three) + Neither
THIRD FORMULA-
TOTAL = ( Exactly one group ) + ( Exactly 2 groups) + ( All three ) + Neither
I hope this clarifies your doubt
Hello,
I used the same Venn diagram from Param800. Also, my approach is similar to one of the posts answered by rijul007.
https://www.beatthegmat.com/ps-virtual-r ... 09926.html
My approach was as follows:
120 = a + d + e + g
90 = b + d + f + g
225 = c + e + f + g
So, 435 = a + b + c + 2d + 2e + 2f + 3g
= a + b + c + 2(d + e + f) + 3g - Eq. 1
Since 35% experienced at least 2 of these effects,
105 = d + e + f - Eq. 2
Substituting Eq.2 in Eq. 1:
435 = a + b + c + 2(105) + 3g
So, 225 = a + b + c + 3g - Eq. 3
Since 300 subjects participated in the experiment,
300 = a + b + c + d + e + f + g
So, 300 = a + b + c + 105 + g (from Eq. 2)
So, 195 = a + b + c + g - Eq. 4
Substituting Eq. 4 in Eq. 3,
225 = a + b + c + g + 2g
= 195 + 2g
2g = 30
g = 15
Substituting g = 15 in Eq. 4,
195 = a + b + c + 15
So, a + b + c = 180
I was wondering if this approach is correct?
I was confused was the question says 35% experienced exactly 2 of these effects. Hence I take:
105 = d + e + f (where 105 = 35% of 300)
Is this correct? I was first thinking that it should be 105 = d, 105 = e, 105 = f but then got a feeling that this would be incorrect. I think this is similar to what the question is asking i.e. how many of the subject experienced only one of these effects? i.e. how many experienced a or b or c?
Is this understanding correct? Thanks.
Best Regards,
Sri
