A rather fundamental concept which I somewhat failed to grasp and now is jeopardising my further understanding/solving of probability problems..
In the case of this question, where we are to find the probability, that the minimum of two throws of a fair die equals $k$, $k \leq 6, k \in \mathbb{N}$, do we have to account for the ordering of the dice?
I.e., assuming $k = 3$, is the probability $P(\{3\}) = \frac{1}{6}\times\frac{4}{6}\times 2$ in order to account for the fact that the first throw could be $3$ and the second throw anything from $3$ onwards OR vice versa (the first throw anything from $3$ onwards and the second throw $= 3$)? Or should it just be $P(\{3\}) = \frac{1}{6}\times\frac{4}{6}$ since the dice are similar and there is no mention that the two dice are unique (e.g. different in colour, size etc.).
The general question, hence, is, for cases where coins/dice are involved and are not uniquely labelled, should the order be regarded, if there is no additional mention of a first/second throw?
Hope you all get my drift..