Profits from an outdoor sporting event are affected by inclement weather.The promoter of the event expects it to net a profit of $7,500,000 if the weather is dry, but only $20,000 if the weather is wet.The historical probability of rain is 5% for the day of the event.

a) What is the expected profit from the event?Show all work.

b) The promoter can buy $500,000 weather protection insurance for a premium of $50,000 (In other words, the promoter pays $50,000; then if it rains, the insurance company pays the promoter $500,000; however, if it does not rain, the insurance company pays nothing.)Based on expected profit, would it be wise to buy insurance?Show all work and explain your reason

c) Suppose the chance of rain is 20% and the insurance costs $70,000 for the $500,000 policy. Based on expected profit, would it be wise to buy the insurance under these weather conditions?Show all work and explain your reason