Question

this week in school, there is a 75 percent probability of having a fire drill, a 50 percent probability of a tornado drill, and a 25 percent probability of having both drills. let event f be a fire drill and event t be a tornado drill. are the two events independent? no, because p(f ∩ t) ≠ p(f)·p(t). no, because p(f ∩ t) ≠ p(f)+p(t). yes, because p(f ∩ t)=p(f)·p(t). yes, because p(f)=p(t)+p(f ∩ t).

Explanation:

Step1: Identify given probabilities

$P(F)=0.75$, $P(T) = 0.5$, $P(F\cap T)=0.25$

Step2: Calculate $P(F)\cdot P(T)$

$P(F)\cdot P(T)=0.75\times0.5 = 0.375$

Step3: Compare $P(F\cap T)$ and $P(F)\cdot P(T)$

Since $P(F\cap T)=0.25$ and $P(F)\cdot P(T)=0.375$, $P(F\cap T)
eq P(F)\cdot P(T)$

Answer:

A. No, because $P(F\cap T)
eq P(F)\cdot P(T)$