To expand the probability union P(A∪B∪C∪D) for non-disjoint events, the correct approach involves adding the probabilities of each event, subtracting the probabilities of all pairwise intersections, and then adding the probabilities of all triple intersections while subtracting the probability of the intersection of all four events. The discussion highlights confusion between independent and disjoint events, clarifying that independence means the occurrence of one event does not affect the others, while disjoint events cannot occur simultaneously. For independent events, the probability can be calculated using the formula P(A∪B∪C∪D) = 1 - [1-P(A)][1-P(B)][1-P(C)][1-P(D)]. The conversation also emphasizes the complexity of calculating probabilities with many events and the importance of understanding the distinction between independence and disjointness. Overall, the participants navigate the nuances of probability theory while seeking clarity on their homework problem.
