For three events $A, B,$ and $C$, we are given $P(A) = 0.5, P(B) = 0.6, P(C) = 0.4$, and the pairwise intersection probabilities are $P(A \cap B) = 0.25$, $P(B \cap C) = 0.15$, and $P(A \cap C) = 0.20$. If the probability of at least one of the three events occurring is $0.95$, what is the probability that all three events occur simultaneously?