Moral Hazard and Uncertainty
Analyze your results
In both cases, alter the probabilities of having an accident or not if you drive carefully or not. Specifically, you have a 30% chance of having an accident if you go carefully and a 70% chance of not having an accident if you drive carefully. Invert these percentages if you drive carelessly.
Do your initial results change, i.e., does having insurance give the person an incentive to drive without caution?