The manager is on the fence about her decision to hire, so she gives the salespe

Question

The manager is on the fence about her decision to hire, so she gives the salesperson a trial period. The candidate sells 2 cars in the week-long trial period. Even a great salesperson can go through a dry spell, so there is still a chance that the candidate is a great salesperson. A great salesperson has a 10% chance of selling only 2 cars in one week. Likewise, a mediocre salesperson has a 40% chance of selling only 2 cars in one week, and a poor salesperson has an 70% chance of selling only 2 cars in one week. (d) Using this new information, determine the posterior probabilities of the candidate being great, mediocre, and poor. (e) What should the manager's decision be after her observation?

Explanation / Answer

d) Probability of employee selling only 2 cars in week = (0.10 + 0.40 + 0.70) / 3 = 0.40

here division by 3 is done as an employee has equal chance of being great, mediocre or poor

posterior probability for:

1. Great = (0.10*0.33)/0.40 = 0.0833

2. Mediocre =(0.40*0.33)/0.40 =0.3333

3.Poor=(0.70*0.33)/0.40 = 0.5833

e)She should not hire the employee as the chance of him being a poor salesperson is most.

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