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MoStGu joins AYG, an multinational insurance company, as a management trainee after his graduation. The number of insurances MoStGu sells at AYG follows a Poisson

MoStGu joins AYG, an multinational insurance company, as a management trainee after his graduation. The number of insurances MoStGu sells at AYG follows a Poisson distribution, with mean 5 per month. In an effort to motivate its trainees, AGY implements the following promotion structure: If 3 or more insurances are sold by a trainee in a month, the month is considered a "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.

What is the probability that a month is a success?

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?

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