Mutually exclusive are the events which cannot happen at the same time.

For example: when tossing a coin, the result can either be heads or tails but cannot be both.

Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of the other(s).

Eg: Rolling a die and flipping a coin. The probability of getting any number on the die will not affect the probability of getting head or tail in the coin.

So, if A and B are event is independents any information about A can not tell anything about B while if they are mutually exclusive then we know if A occurs B does not occur.

So independent events cannot be mutually exclusive.

Now to test if probability of independent events is 1 or not

Consider an example:

Let A be the event of obtaining a head.

P(A) = 1/2

B be the event of obtaining 5 on a die.

P(B) = 1/6

Now A and B are independent events.

So, P(A) + P(B)

Hence P(A) + P(B)≠ 1

It is true in every case when two events are independent.

Hence option D is correct.