This week in school, there is a 75 percent probabiity of having a fire drill, a 50 percent probability of a tornado drill, and a 25 percent probability of having both drils. Let event \( F \) be a fire drill and event T be a tornado drill. Are the two events independent? No, because \( P(F \cap T) \neq P(F)=P(T) \). No, because \( P(F \cap T) \neq P(F)+P(T) \). Yes, because \( P(F \cap T)=P(F)=P(T) \). Yes, because \( P(F)=P(T)+P(F \cap T) \).

To determine if the events are independent, we examine the relationship between the probabilities. For two events to be independent, the probability of both events occurring together should equal the product of their individual probabilities: \( P(F \cap T) = P(F) \cdot P(T) \). Here, \( P(F) = 0.75 \) and \( P(T) = 0.50 \), so \( P(F) \cdot P(T) = 0.75 \cdot 0.50 = 0.375 \). However, we are given \( P(F \cap T) = 0.25 \). Since \( 0.25 \neq 0.375 \), the events are indeed dependent! In real life, understanding the independence of events can prove useful in safety protocols. For instance, when planning drills in schools or workplaces, knowing if certain emergencies coincide can help in creating more effective safety plans. If fire and tornado drills are independent, preparations might differ, creating tailored responses that enhance safety outcomes during actual emergencies.