The distribution of income and wealth resulting from risk-taking behavior significantly affects cooperation and risk-sharing in many areas in many governmental programs, including health insurance and agricultural production. This paper studies redistributive decision making and fairness preferences under different rooted risks using a laboratory experiment, in the treatment of which the subjects can endogenously determine whether they want to buy insurance before they face one of three possible outcomes that will be realized with equal probability. If the first outcome is realized, a high payment will be delivered regardless of whether the subject buys insurance or not. The second risk is an avoidable loss contingent upon the subject buying insurance. The third outcome is an inevitable loss, i.e., minimum payment will be delivered no matter if the subject has or does not have insurance. Then we investigate fairness preferences of randomly paired subjects who are informed about the choices and outcomes for both parties and are asked to make redistributive tasks. The experimental design mimics the scenario of risk-sharing in health insurance and agricultural production. We find that how people make redistributive decisions depends on the insurance purchase decisions and income inequality. The results provide some policy implications for improving insurance efficiency.