This is not an experiment question as such, it's more of a puzzle - a bit of fun with venn diagrams and conditional probability.

I used to think of independent events as examples where the events were physically disjoint - for example I throw a die in my house and you toss a coin in yours. But it turns out that there are infintely many pairs of events that are phyically connected and independent.

This activity concerns a school in which some students study both History and Geography. Some others study just one of these subjects, and some others study niether. Your challenge is to adjust the numbers in each set to create independent events, that is, P(H)=P(H|G), and ultimately find a formula that generates the solutions.