Mutually exclusive and independent events are where my train gets stuck. So this is the definitive attempt at establishing the difference. The crux is that independence comes into effect if there are more than one events as part of the experiment! If there is just one event, then its just a question of exclusivity.

What is the probability of getting a head after tossing a coin OR picking out an ace from a deck of 52 standard playing cards?
Ans: These two events are INDEPENDENT! Hence the question doesn’t make sense. The answer is EITHER the probability of the first event or the probability of the second event. Each experiment is separate and the outcomes are separate.

What is the probability of picking an ace OR picking a king from a deck of cards?
Ans: These two probabilities are part of the same event! Moreover, they are exclusive. Each card in a deck for that matter has its neat little space which does not interfere with the other’s space. Hence we can add the probability of each and get the answer.