Let's say that a certain measure 'X' has a 60% chance of preventing an event and another measure 'Y' has a 70% chance of preventing the same event. Let's say that both measures are used, then what would be the odds of preventing that same event if the options are a.independent and b.dependent?
Another way of answering this question would be supposing the measures run one after the other and adding the probability of X preventing the event (60%) and the probability of Y preventing the event after X has failed to do so. That's 40% (probability of X not preventing the event) times 70% (probability of Y stopping the event).
This is $0.6 + 0.4\times0.7 = 0.6 + 0.28 = 0.88$
When you have many measures to consider, working with disjoint sets is, in my opinion, a lot easier
If the events are independent then we use the familiar formula,
$P(X \cup Y)= P(X)+P(Y)-P(X \cap Y)$