Probability: mutually exclusive events A+B+neither = 1?

GRE Quant Problem Solving
1

Hypothetical,

If I have event A with a probability of x, and event B with a probability of y, could it be possible that

P(A) + P(B) =/= 1 if probability of neither > 0

Example: six sided die is rolled. P(2)= 0.166667, P(4) = 0.166667, P(neither) = 0.666667. What is P(2) + P(4)? 0.3333…

hypothetical 2:
If a question doesn’t mention “neither” as a possibility, should I assume I’m only dealing with a
P(A) +P(B) = 1 situation?

2

Yes, this is a correct way of looking at it. Another way would be that the probability of ALL mutually outcomes adds to 1. Since 2 and 4 are not the only outcomes of rolling a die, their probabilities won’t add to 1.

3

Thank you!