At a nationwide travel agency, newly hired employees are classified as beginners (B). Every six months the performance of each agent is reviewed. Past records indicate that transitions through the ranks to intermediate (I) and qualified (Q) go according the following Markov chain, where (F) stands for "fired": B I Q F B 0.45 0.4 0 0.15 I 0 0.6 0.3 0.1 Q 0 0 1 0 F 0 0 0 1 (i) What fraction of beginners are eventually qualified? (ii) What is the expected time until a beginner is fired or become qualified? (iii) What fraction of intermediates are eventually qualified? (iv) What is the expected time until an intermediate is fired or become qualified?