Totally lost of where to start with this question :
Suppose you roll three distinguishable fair dice and call the resulting numbers a, b, and c. Define events X= “a+b is even", ”Y= “b+c is even", and Z= “a+c is even”. Prove that these three events are pairwise independent but not mutually independent.
Right now, this is how I understand the difference between pairwise independence and mutual independence.
𝐴,𝐵,𝐶 are mutually independent if $𝑃(𝐴∩𝐵∩𝐶)=𝑃(𝐴)𝑃(𝐵)𝑃(𝐶)$
But this is not the case for pairwise independence.
Any help would be greatly appreciated!