You are considering purchasing car insurance that costs $$800.$ You don't want to be a "chump" if you don't have to be$.$ You do some research, and you find out

that there's only a $3\%$ chance that you will get in a serious accident costing $$500$ in damages with insurance, but $$13,000$ without insurance. The potential for a

small accident costing $$300$ in damages with or without insurance is $7\%.$ The other $90\%$ of the time, it is not probable you would wreck, and thus you would

expect $$0$ in damages. Should you pay into insurance, or should you take the risk and buy no car insurance at all? Draw a decision tree and show your work to

support your claim. All values are Present Worth costs. $(25$ points$)$

EXTRA CREDIT: Why do engineers sometimes use decision trees? $(2$ points$)$