1. MoStEu joins AYE, an multinational insurance company, as a management trainee after his graduation. The number of insurances MoStGu sells at ATE follows a Poisson distribution, with mean 5 per month. In an effort to motivate its trainees, AG? implements the following promotion structure: If 3 or more insurances are sold by! a trainee in a month, the month is considered a r'Success" month for this trainee. In the next 12 months [evaluation period], a trainee will be promoted to manager if he has 10 or more success months. Assume that the sales in each month are independent of sales in other months. ta] [2 points] What is the probability! that a month is a success? (b) [5 points] AYG currently has four management trainees (including MostGu). The sales of each of the other three trainees also follow a Poisson distribution with mean 5 per month and the sales of all trainees are independent across trainees. What is the probability that exactly 3 trainees will be promoted to manager at the end of evaluation period