The addition rule of probability says that the probability that event A or event B occurs equals the sum of their individual probabilities minus the probability that they both occur together.

Core idea

  • Formally, the general addition rule is
    P(A or B)=P(A)+P(B)−P(A and B)P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B)P(A or B)=P(A)+P(B)−P(A and B).
  • This rule ensures that any overlap (outcomes counted in both A and B) is not double-counted, so that the final probability is correct.

Special case: mutually exclusive events

  • If A and B are mutually exclusive (cannot happen at the same time), then P(A and B)=0P(A\text{ and }B)=0P(A and B)=0, so the rule simplifies to P(A or B)=P(A)+P(B)P(A\text{ or }B)=P(A)+P(B)P(A or B)=P(A)+P(B).
  • In words: for mutually exclusive events, the addition rule says the probability of A or B is just the sum of their probabilities.

How to recognize it in options

The best description among answer choices will usually look like:

“The probability that A or B occurs equals the probability of A plus the probability of B minus the probability that A and B occur together.”

This wording captures the general addition rule of probability, including the overlap term.

TL;DR:
The correct statement is the one that says:
P(A or B) = P(A) + P(B) − P(A and B).

Information gathered from public forums or data available on the internet and portrayed here.