Question: In Exercise we asked (among other things), if a student knows 80% of the material in a course, what is the probability that she answers a question correctly on a 100 question True-False test (assuming that she guesses on any question she does not know the answer to)? (We assume that she knows what she knows, that is, if she thinks that she knows the answer, then she really does.) Show how we can use a probability tree to answer this question.
Exercise: Sometimes information about conditional probabilities is given to us indirectly in the statement of a problem, and we have to derive information about other probabilities or conditional probabilities. Here is such an example. If a student knows 80% of the material in a course, what do you expect her grade to be on a (wellbalanced) 100 question short-answer test about the course? What is the probability that she answers a question correctly on a 100 question true-false test if she guesses at each question she does not know the answer to? (We assume that she knows what she knows, that is, if she thinks that she knows the answer, then she really does.) What do you expect her grade to be on a 100 question True-False test to be?