Each of the 20 questions at the Final Exam is estimated by 10 points. For each question independently, a student has 40% to answer correctly and receive 10 points, and 20% chance to get paritial credit of 5, 2, or 0 points. To pass the exam, the student must get 101 or more totally.
(a) What is the probability to fail the exam?
(b) What is the probability to fail on this exam if instead of 20 questions the test contains n questions and n
∞?