Risk is the measure of uncertainty about the future payoffs of an investment, measured over certain time horizons and relative benchmarks.

Question: Apply the definition of risk provided in the textbook to an individual's decision to purchase a car insurance policy. Suppose that the individual has two possibilities: no accident ($0 gain/loss) and accident (-$30,000 loss). If the probability of an accident is lower than the probability of an accident occurring (say the probability of an accident is 10%),then, why do people buy car insurance? How is this related to the concept of value at risk and the time horizon of investment decisions?