Question

determining if events are independent 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 cap t)
eq p(f) cdot p(t) ) no, because ( p(f cap t)
eq p(f) + p(t) ) yes, because ( p(f cap t) = p(f) cdot p(t) ) yes, because ( p(f) = p(t) + p(f cap t) )

Explanation:

Step1: Recall independence formula

Two events \( F \) and \( T \) are independent if \( P(F \cap T) = P(F) \times P(T) \).

Step2: Identify given probabilities

\( P(F) = 0.75 \), \( P(T) = 0.50 \), \( P(F \cap T) = 0.25 \).

Step3: Calculate \( P(F) \times P(T) \)

\( P(F) \times P(T) = 0.75 \times 0.50 = 0.375 \).

Step4: Compare with \( P(F \cap T) \)

\( P(F \cap T) = 0.25 \), and \( 0.25
eq 0.375 \), so \( P(F \cap T)
eq P(F) \times P(T) \), meaning events are not independent.

Answer:

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