Use your common sense to answer this question. Are the events "Rain" and "Having a Car Accident" independent or dependent?
There are three equivalent definitions of independence. The two mathematical definitions are:
However, the third definition is the most helpful for "common sense" questions like this:
3) Knowing the outcome of one variable gives you no information about the outcome of another.
Think about rain and car accidents. If I told you that it was raining heavily, would you think differently about my chances of being in a car accident than if I told you the sun was shining? If yes, then the two variables CANNOT be independent of each other and therefore must be dependent.