How to find similarity ratio?

Question

Helllo,

I am not very good in math and I have simple question

My question is:

say I have 2 groups (A and B), where A has 17 pens (for example) and B has 13 pens. If 12 pens were the same from A and B, How can I present this in ratio?

Thank you

Answer 1

There are four groups: A with size 17, B with size 13, their intersection with size 12 and their union with size 17+13-12=18 (being size A + size B - size intersection). The intersection is subtracted in determining the union size, because it is the overlap of A and B and would otherwise be counted double. An often used similarity index divides the intersection size by the union size.

Jaccard would give: 12/(17+13-12)=12/18=2/3