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A student at a certain university will pass the oral Ph.D. qualifying ex-amination if at least two of the three examiners pass her or him. Past experience shows that (a) 15% of the students who take the qualifying exam are not prepared, and (b) each examiner will independently pass 85% of the prepared and 20% of the unprepared students. Kevin took his Ph.D. qualifying exam with Professors Smith, Brown, and Rose. What is the probability that Professor Rose has passed Kevin if we know that neither Professor Brown nor Professor Smith has passed him? Let S. B, and R be the respective events that Professors Smith, Brown, and Rose have passed Kevin. Are these three events independent? Are they condi-tionally independent given that Kevin is prepared?

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