Fire insurance policy

Your current salary is a fixed sum of $115,600 per year. You have an offer for another job. The salary there is a flat $75,000 plus a chance to earn $350,000 if the company does well. Assume that your utility from income can be expressed as U=income. So, for example, at an income level of $100, your utility level is 10; your utility level from the current salary of $115,600 is 340. How high does the probability of success for the company have to be to induce you to take this job?

At the beginning of 2015 I bought a fire insurance policy for my vacation home in Aspen; at the end of the year, my vacation home had not burned down. Was my purchase a mistake? Explain.