1- Decision Analysis (20 points) Ella just returned from overseas. She was advised to self-quarantine, but she missed her friends and wants to hang out with them. Considering the flights she took and time spent at airports, she has 30% risk of carrying corona virus. If she turns out to be a carrier of corona virus and spends time with her friends, she will infect her friends. If she isn't a carrier of corona virus and spends time with her friends, no one is going to be infected. The utility from various actions/events are listed in the table below: Utility Self-quarantine 60 Hang-out with friends and no one is infected 100 Hang-out with friends and friends get infected -30 a. (5 points) If Ella is a utility maximizer, should she shelf-quarantine or hang-out with friends? Explain. Recently, a Covid-19 test is developed. It is very effective, but it is not 100% reliable. If the person is a carrier, the test identifies the person as carrier in 95% of the cases. If the person is not coronavirus carrier, the test identifies the person as not a carrier in 85% of the cases. b. (5 points) If Ella takes the Covid-19 test and the test identifies her as a carrier, what is the probability that she is actually a Covid-19 carrier? C. (10 points) Administering the Covid-19 test is stressful and painful. Ella thinks that the utility of administering the Covid-19 test is -10 for Ella. Assume additive utility. For instance, if Ella takes the tests and decides to self-quarantine, her utility will be (-10)+60 = 50. Should Ella take the test? Show your work