There is a subject-naturally not Math for Computer Science-in which 10% of the assigned problems contain errors. If you ask a Teaching Assistant (TA) whether a problem has an error, then they will answer correctly 80% of the time, regardless of whether or not a problem has an error. If you ask a lecturer, he will identify whether or not there is an error with only 75% accuracy. We formulate this as an experiment of choosing one problem randomly and ask- "mes" - 2018/6/6 - 13:43 - page 840 - #848 Chapter 18 Conditional Probability ing a particular TA and Lecturer about it. Define the following events: E ::= [the problem has an error], 7 ::= [the TA says the problem has an error], L ::= [the lecturer says the problem has an error]. (a) Translate the description above into a precise set of equations involving con- ditional probabilities among the events E, T and L. (b) Suppose you have doubts about a problem and ask a TA about it, and they tell you that the problem is correct. To double-check, you ask a lecturer, who says that the problem has an error. Assuming that the correctness of the lecturer's answer and the TA's answer are independent of each other, regardless of whether there is an error, what is the probability that there is an error in the problem? (c) Is event 7' independent of event _ (that is, Pr [7 | = Pr)? First, give an argument based on intuition, and then calculate both probabilities to verify your intuition