I've some confusion about when to use which approach for calculating the conditional probabilities.
Case 1: why not just directly 2/6 and need to use the multiplication rule? It seems to me just simple counting. In this case both 2/6 and the conditional multiplication gives the same result. Is that just a coincidence? And what exactly are the relationship between these 2 methods?
Case 2: When do we use numbers, or percentage as both the numerator and denominator of conditional probabilities? In contrast with case 1 above, when do we know we need to just do simply counting on the numbers/probabilities to construct our conditional probabilities and when to apply multiplication rules? I think the boundaries between those two are very blur to me.
Specifically, I'm wondering what are the conditions for using either approach? And what's the relation between these approaches? TIA.