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, they will identify whether or not there is an error with only 75% accuracy. for each problem, assume that the correctness of ta’s and lecturer’s responses are independent of each other. we formulate this as an experiment of choosing one problem randomly and asking a particular ta and lecturer about it. define the following events: e : : = [the problem has an error], t : : = [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 conditional 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. what is the probability that there is an error in the problem? (c) is event t independent of event l? first, give an argument based on intuition, and then verify your intuition with calculations.