What is the probability formula for determining the chance that neither event A nor event B will occur?

To determine the probability that neither event A nor event B occurs, we can utilize the principle of complementary probabilities. The probability of at least one of the events A or B occurring is represented by P(A or B). Therefore, the probability that neither event occurs would be the complement of this probability.

Mathematically, this is expressed as follows:

P(neither A nor B) = 1 - P(A or B).

This relationship takes into account all possible outcomes, ensuring that if we subtract the probability of either event occurring from 1, we are left with the probability of both events failing to occur. The option identified correctly reflects this fundamental concept in probability.

Understanding this helps clarify the interrelated nature of probabilities and the importance of complementary events, as well as how they can be calculated to derive meaningful insights on independent and combined occurrences.