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1. Mary joins ABC, a car dealership company, as a management trainee. The number of cars that Mary sells at ABC follows a Poisson distribution, with an average of 5 cars per month. To motivate trainee, ABC implements the following promotional structure: If a trainee sells 3 or more cars in a month, that month is considered a "successful" month for that trainee. During the next 12 months (assessment period), if the trainee has 10 or more successful months, she will be promoted to manager. Assume that each month's sales are independent of other months' sales.
(a) What is the probability of success in one month?
(b) ABC currently has four management trainees (including Mary). The sales of the other three trainees also follow a Poisson distribution, averaging 5 times per month, and the sales for all trainees are independent across trainees. What is the probability that exactly 3 trainees will be promoted to managers at the end of the evaluation period?
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