Question 1 (10 marks) Suppose that a university student has to take 10 independent courses in the final year. The class of honors awarded is based on the results of the final year examination. If a student gets Aor above for at least 8 courses, he/she will be awarded a first class honors.

Under ordinary circumstances, John will get Aor above for at least 8 courses with probability of 0.2. However, with a probability of 0.3, John will be in a low mood during the examination period. Under that low mood case, John will get Aor above for each course with probability 0.45.

(a) What is the probability that John will get Aor above for at least 8 courses given that he is in low mood during the examination period? (6 marks) (b) What is the probability that John will achieve a first class honors? (4 marks)