uppose 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 A or above for at least 8 courses, he/she will be awarded a first class honors.

Under ordinary circumstances, John will get A or 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 A or above for each course with probability 0.45.

(a) What is the probability that John will get A or above for at least 8 courses given that he is in low mood during the examination period?

(b) What is the probability that John will achieve a first class honors?