3. [45] A large fast-food company regularly Opens new outlets. Many of these new outlets fail, however, and are closed within three years. The company is trying to study the process of success and failure in order to predict the overall costs of opening a certain number of successful new franchises, improving the success rate, and so on. There is considerable dependence of the failure rate on the experience and previous success of the manager of the new outlet. Managers attempting their rst new outlet have a failure rate of 40%; managers who succeed on their rst attempt have a failLu'e rate on their second attempt of only 25%, and managers who succeed on their first two attempts have a failure rate on their third and subsequent attempts of only 20%. The rate stabilizes at 20% then and for all future attempts; it seems that additional experience does not allow managers to improve their failure rates further. Managers who fail on their rst attempts have a failure rate on the second attempt of 50%1 and those who fail on their rst two attempts have a failure rate on the third and all subsequent attempts of 60%. I will use the term 'successful manager' for managers who succeed on their rst two attempts, and 'unsuccessful manager1 for those who fail on their rst two attempts. Of course, there will also be some managers will succeed on one and fail on the other the rst two attempts. a) Andrea is a successful manager. After her first two new outlets are established, she is given three more to try over the next years of her career. If all five of these succeed, she will be promoted to regional manager. Find the probability that she gets promoted. b) Belinda is a new manager who has never attempted to open a new outlet. Find the probability that she will open three successful new outlets on her first three attempts. c) Find the probabilities that (i) Belinda will turn out to be an unsuccessful man- ager; (ii) that she will have exactly one failure in her first three attempts. d) There isn't enough information here to calculate the overall failure rate of new outlets. What new information would be sufficient to allow you to make this calcula- tion