What formula represents the calculation for the probability of at least one event occurring for two independent events?

The calculation for the probability of at least one event occurring for two independent events can be represented by the inclusion-exclusion principle. The correct formula combines the probabilities of the individual events and accounts for any overlap between them to avoid double-counting.

In the case of two independent events, the probability of at least one event occurring is calculated as follows:

P(at least one event occurs) = P(Event1) + P(Event2) - P(Event1 AND Event2).

This formula correctly adds the probabilities of both events occurring independently while subtracting the joint probability of both events occurring, which has been counted twice.

The reasoning behind this approach is foundational in probability theory, as it addresses the relationship between independent events. If the events are indeed independent, the probability of both occurring simultaneously can be determined by multiplying their individual probabilities (i.e., P(Event1) * P(Event2)). However, when we're looking for the probability of at least one happening, we need to ensure we don't count that joint occurrence twice.

Thus, the correct choice reflects this understanding and uses formal probability principles to arrive at an accurate calculation for the scenario described.