2. There are 100 servers in the company, 80% are up to date with their patches. Data shows that if a server is up to date with its patches, there is a 10% chance that it will be compromised. Data also shows that if a server is not up to date with its patches, there is a 70% chance that it will be compromised. Let Up stand for "up to date with patches" and C stand for "compromised". Construct a tree diagram to answer the questions below a. Insert a photo of your tree: Place all 10 probabilities on the correct part of the tree in order to get full credit. b. What is the probability that if you randomly select a server you will find that it is up to date with its patches and it is compromised? Use the identified events and set notation to set up your problem. c. What is the probability that if you randomly select a server you will find that it is not up to date with its patches and it has been compromised? Use the identified events and set notation to set up your problem. d. What is the probability that a randomly selected server has been compromised? Use the identified events and set notation to set up your problem e. What is the probability that if you randomly select a server from those that have been compromised, you will find that it is up to date on its patches? Use the