A worker has asked her supervisor for a letter of recommendation for a new job.

Question

A worker has asked her supervisor for a letter of recommendation for a new job. There is an 80% chance that she will get the job offer if she receives a strong recommendation, a 40% chance that she will get the job offer if she receives a moderately good recommendation, and a 10% chance that she will get the job offer if she receives a bad recommendation. Further, the probabilities that the recommendation will be strong, moderately good, or weak are 0.7, 0.2 and 0.1, respectively.

(i) What is the probability that the worker will get the job offer?

(ii) Given that she does get the job offer, what is the probability that she received a moderately good recommendation?

Explanation / Answer

(i) (0.7)((0.8) + (0.2)(0.4) + (0.1)((0.1) = 0.65

(ii) P = (0.2)(0.4) / 0.65 = 0.123

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