In a probability experiment, events a, b, and c have probabilities p(a) = 0.3, p(b) = 0.4, and p(c) = 0.5, respectively. Events a and b are disjoint, events a and c are independent, and the conditional probability of event b given event c is p(b|c) = 0.1. Find the probability of the union of events a, b, and c (p(a ∪ b ∪ c)).