Is this conditional probability question missing information to be able to solve? I attached an image of what I to try to solve it with a tree diagram. D is the event that a person fits the description, I is the event the person is innocent. But, I can't figure out what to put other portions of the diagram. Is there a better way to visualize the problem? For example, should a start the diagram with the event being innocent?
"Someone in the maths department has stolen a cookie from the statistics research group's biscuit tin. The thief was not as smart as they thought they were though: They were seen by a decorator who was painting the room in which the biscuit tin is stored. The decorator provided a detailed description of the thief, and this description fits only 2.5% of staff in the maths department. Chris is one of the staff members fitting the description, and is accused of having stolen the cookie."
Question:
What is the probability that Chris is innocent, given that he fits the thief's description?
In the previous question I am asked the following and got the correct answer. "If there are 120 members of staff in the department, how many fit the description?" But, the question that I am particularly struggling with does not say to use the same scenario of 120 people. Thank you.