Emily is in the final semester of her studies at the University. She has completed successfully all compulsory courses needed for her degree and shemust pass at least four exams to finish her studies among seven possible optional courses offered. The probability of passing an exam in any course she takes is p = 4∕5, but exams vary in difficulty. More specifically, Emily feels that in order to pass the first two exams she needs to study a further 15 hours for each, for the next three she has to study 20 hours for each course, while for each of the last two exams she has to study 25 hours. Assuming that she knows the outcome of each exam immediately after the exam finishes, she is obviously not willing to sit any further exams as long as she has passed four.

(i) What is the probability that she takes all seven exams?

(ii) Find the expected number of hours she needs to study from now.