When do we add and when do we multiply probabilities?

We add probabilities when the corresponding events are alternatives, e.g. P(rolling a 4 on a pair of dice) = P(rolling a 1 and a 3) + P(rolling a 2 and a 2). These are mutually exclusive events which can't happen at the same time.We multiply probabilities when corresponding events happen consecutively or at the same time, e.g. P(it will rain tomorrow and the day after tomorrow) = P(it will rain tomorrow) * P(it will rain the day after tomorrow). We can do this so long as the events are independent, i.e. they do not affect one another.