How to express sample space

Question

I have been given

$$P(A\mid B) = P(A)$$ $$P(C\mid D) < P(C)$$ $$P(E\mid F) > P(E)$$

and have been asked to give an example of a sample space. My question is how can I go about expressing a sample space with this information? I am unsure of where to begin with this question and would like general hints or instructions on how to do this.

No answers though please!

Answer 1

Give an example of any sample space containing six events such that you can affirm that those three probability statements are true.

Hint: what do those statements say about the dependence of each pair of events?

Answer 2

Translating into an intuitive language, the first one means that it would not change the likelihood of $A$ whether you know $B$ occured. As for the second and third ones, the new information you acquired (namely, $D$ and $F$) forces you to update your calculations.

Now consider a die rolling scenario.