A teacher has four students with the last name “Ronaldo”. Over the course
of the school year, they regularly submit extra credit quizzes. Andrew Ronaldo answers an average of 95% of quiz questions correctly, Bruno Ronaldo answers an average of 90% correctly, Cristiano Ronaldo averages 85% correctly, and Diego Ronaldo averages 80% correctly. 40% of received quizzes come from Cristiano and 40% come from Diego, because they really need the extra credit. 15% of received quizzes come from Bruno and 5% come from Andrew.
The teacher ﬁnds a stack of quizzes to grade from one of the Ronaldo students, but the ﬁrst name is missing. He randomly selects 30 questions from the stack and grades them, ﬁnding that 2 are incorrect and 28 are correct.
(a) If the stack of quizzes is from Andrew, what is the probability that exactly 2 out of the 30 randomly chosen questions would be incorrect?
(b) What is the probability that this stack of quizzes is from Andrew?
(c) Which student is most likely to have submitted the stack of nameless quizzes?