Yup, that looks good

60+50+35 = 145
145-10(2) = 125
125-100 = 25
25% of customers purchase 2 of the above products

P1 - one product, P2 - two poducts, P3 - three products

P1+P2+P3 = 100
P1+2*P2+3*P3 = 60+50+35 = 145
P3 = 10 -> P2 = (145-100)-2*10 = 45-20 = 25 -> D

Venn Diagram is my favorite here. Slow but true.

10= All 3
CA: A-10
MA: C-10
CA: B-10

M: 60 - (A-10+10+C-10) --> 70-A-C
C: 50 - (A-10+10+B-10) --> 60-A-B
A: 35 - (B-10+10+C-10) --> 45-B-C

Add everything


70-A-C
60-A-B
45-B-C
A-10
B-10
C-10
10
--> 155-A-B-C=100 ---> A+B+C=55 Now we want only 2 items so now its just A+B+C-30 =25

D

Can someone provide the standard formula for 3 Venn diagram and 2 Venn Diagram.

Thanks
JAck

i'm also a bit confused by everyone else's work, this is the way I solved it

the equation is

P(A or B or C ) = P (A) + P (B) + P (C) - P(A & B) - P(A & C) - P(B & C) + P (A & B & C)
also, the probability of A or B or C is 100% since A,B,C are the only sets in this space.

when you add up P(A), P(B), P(C), you are also over adding in case they have intersections of 2 or 3 *draw a venn diagram with 3 intersection circles and it can help make sense . Therefore you subtract out the places where two of them overlap. However, as you were subtracting the 2 set overlaps, each time you're subtracting any 3 set overlap as well. So you end up subtracting 3x for the 3-set overlap there, but recall in the beginning you added 3x for the 3-set overlap for A,B,C, so net is zero for that 3 set overlap. You can't ignore the 3-set overlap so you add it back in as the last component.

Anyway, the problem goes

60+50+35 - (2 set overlaps) + (3 set overlap) = 100
145 - (2 set overlaps) + 10 = 100
155 - (2 set overlaps) = 100
(2 set overlaps) = 55

That means that 2 set overlaps add up to 55%. Meaning P(A&B) + P(A&C) + P(C&B) = 55

What's important here is you're back to the same problem of over adding because there are probabilities where all 3 sets overlap. so if you notice you're actually adding the 3 set overlap 3x, once in each term obviously. Now normally you would think ok, I have to subtract the 3-set overlap out 2x, leaving just net 1. And that would be 100% correct if you are looking for Probability of people buying 2things AND 3 things. But the question asks for only people that buy both (in other words the two set overlaps).

Therefore you would subtract 55 - 3(3 set overlaps) = 25% getting rid of the 3 set overlaps entirely.

@Karishma:

How did you get:

"45 = x + y + z + 2*10
x+ y + z = 25"

I lost the part here..