Kayla takes Nate out for a day of sailing. She rents a boat for a daily fee of $500, and the agent asks if she wants to add insurance for an extra $100. Insurance would cover the cost of a tow in case the boat capsizes; with no insurance the tow fee is $1,500. For each problem below, show all your work and explain your reasoning. A Kayla checks the windspeed, and finds it to be 15 knots, so she estimates a 3% chance of capsizing. Make an expected-value argument about why, or why not, Kayla should buy the insurance that day. (Hint: set up two cases, the expected cost with insurance and the expected cost without. Which tums out to be lower?)