The all-season tires should last 50,000 miles and you expect your tire cost to a

Question

The all-season tires should last 50,000 miles and you expect your tire cost to average about $125 per year. You estimate, given the accident rate of drivers your age, there is an annual 2% chance you will have a minor accident that costs $3125 (with tires) and a 2% chance you will total your car at a cost of $15,125. And, of course, a 96% chance you will only be out $125 worth of tires. The sticky summer tires are a little less expensive but are only rated for 30,000 miles so you expect your tire cost to average about $300 per year. The grip is so much better (shorter stopping distance and higher cornering force), though, that you estimate you'll be able to avoid more accidents. You estimate a 1% chance of a minor accident that costs $3300, and a 1% chance you will total your car at a cost of $15,300. And of course, the 98% chance your costs will just be $300. Which tire should you buy, and what is the difference between the expected values of each tire as an EUAW? a. The summer tire, by S5.50 b. The all-season, by $175 c. The all-season, by $525 d. The all-season is cheaper [by some other amount], but you should buy sticky summer tires for your sports car anyway!

Explanation / Answer

EUAW of All Season Expensive Tyres = 0.02x3125 + 0.02x15125 + 0.96x125 =$62.50 + 302.50 + 120 =$485

EUAW of Sticky Cheaper Tyres = 0.01x3300 + 0.01x15,300 + 0.98x300 =$33 + 153 + 294 =$480

This means that sticky summer tires are cheaper to purchase by $5.0

Hence, option-(a) is the right answer.

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