When using the general addition rule, what must you account for when calculating probabilities of overlapping events?

The general addition rule for calculating the probability of two overlapping events states that to find the probability of either event occurring, you need to add their individual probabilities and then subtract the probability of their intersection. This is necessary because, in overlapping events, the intersection (the scenario where both events occur simultaneously) is counted twice when simply adding the probabilities of the two events. By subtracting the intersection, you adjust the total probability to avoid this double counting.

In this context, the intersection represents the shared probability of the two overlapping events. When you account for the intersection, you ensure that the total probability accurately reflects the occurrence of either event without inflating the chances due to this overlap. This approach helps provide a precise understanding of the likelihood of either or both events happening.