When you purchase your new iPhone3000 for the frugal price of $3000, the salesperson tells you that you should also purchase the all-damages-repaired-for-free warranty. This warranty costs $400, but, at no cost to you, they will replace your phone if it gets broken. You know that you have a 3% chance of breaking your phone during this warranty period. Should you buy the warranty? Why or why not? Back up your answer with mathematical proof.