Mr. Maloy has just bought a new $48,000 sport utility vehicle. Given his health
ID: 335946 • Letter: M
Question
Mr. Maloy has just bought a new $48,000 sport utility vehicle. Given his health conditions, he believes that there is about a 20% chance of being in an accident (that he caused) in the forthcoming year. If he is involved in an accident (he causes), the damage to his new vehicle depends on the severity of the accident (see table). Mr. Maloy is trying to decide whether he is willing to pay $1,000 each year to buy collision insurance with a $2,000 deductible (i.e. He pays the first $2,000 in damages if he causes an accident and the insurance company pays the remainder.) Should he buy the insurance? (Note that if the accident is caused by another person that other person is responsible to pay for the damages to Mr. Maloy’s vehicle.) Therefore there are only two cases –
1. An accident he causes
2. No accident or an accident caused by someone else.
Probability of an accident (he causes) 20% Cost of Insurance $1,000 Deductible $2,000 Type of Accident Cost Cond. Prob. Total $48,000 5% Very Bad $12,000 15% Unpleasant $4,000 20% Little Damage $1,000 60%Explanation / Answer
Mr. Maloy is at risk when he causes an accident. Otherwise there is no risk if there is no accident or accident caused by someone else.
Total risk of accident = Cost*Conditional probability
= 60% * 1000 + 20%*4000 + 15%*12000 + 5%*48000
= 600 + 800 + 1800 + 2400 = $5600
Total payment to be paid by Mr. Maloy = Premium + Deductibe = $ 3000
Since cost of accident > cost of insurance, he should buy the insurance.
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