Assume that you are not required by law to buy car insurance. Then, buying car insurance is a purely economic decision. Also, you need to consider the time value of money in this problem, MARR is 10%.
You are considering buying car insurance for the coming two years. Whether or not you buy insurance, you have the following probability distribution over the car accident damages for each year (the probability of having an accident is independent across years) with 90% chance you will have no accident, with 7% chance you will have a small accident with $300 worth of damage due at the end of the year, with 3% chance, you will have a big accident with $13,000 worth of damage due at the end of the year.
The terms of the insurance: You are covered for the coming two years. Your deductible is $500. Your premiums are due at the beginning of each year (first one is $400 and due now!). Your premium goes up by $50 or $150 if you have a small or big accident respectively. It stays the same if you have no accident. Draw the decision tree that corresponds to the above problem and determine if you should buy insurance or not? (Base your decision solely on the expected values.)