To determine whether two events are independent, we need to check if the probability of both events occurring simultaneously, [tex]\( P(F \cap T) \)[/tex], is equal to the product of the individual probabilities of each event, [tex]\( P(F) \cdot P(T) \)[/tex].
Let's go through the steps:
1. Identify the given probabilities:
- Probability of a fire drill, [tex]\( P(F) \)[/tex] = 0.75
- Probability of a tornado drill, [tex]\( P(T) \)[/tex] = 0.5
- Probability of both drills happening, [tex]\( P(F \cap T) \)[/tex] = 0.25
2. Calculate the product of the individual probabilities:
[tex]\[
P(F) \cdot P(T) = 0.75 \times 0.5 = 0.375
\][/tex]
3. Compare [tex]\( P(F \cap T) \)[/tex] with [tex]\( P(F) \cdot P(T) \)[/tex]:
- [tex]\( P(F \cap T) = 0.25 \)[/tex]
- [tex]\( P(F) \cdot P(T) = 0.375 \)[/tex]
4. Since [tex]\( P(F \cap T) \neq P(F) \cdot P(T) \)[/tex], the two events are not independent.
Therefore, the correct answer is:
No, because [tex]\( P(F \cap T) \neq P(F) \cdot P(T) \)[/tex].
