You have a lottery ticket that has a $45\%$ chance of winning $$10\mathrm{.}00$ and a $55\%$ chance of not winning anything. Your friend has a different lottery ticket with a $20\%$ chance of winning $$25\mathrm{.}00$ and an $80\%$ chance of not winning anything.

Your friend has offered to let you have her ticket if you will give her your ticket plus $$1\mathrm{.}00.$ Draw a decision tree for this decision. What is the Expected Monetary Value $($EMV$)$ of these options, and what should you do$?$