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A worker has asked her supervisor for a letter of
Chapter 3, Problem 51P(choose chapter or problem)
Problem 51P
A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that thcie is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are .7, .2, and .1, respectively.
(a) How certain is she that she will receive the new job offer?
(b) Given that she does receive the offer, how likely should she feel that she received a strong recommendation? a moderate recommendation? a weak recommendation?
(c) Given that she does not receive the job offer, how likely should she feel that she received a strong recommendation? a moderate recommendation ? a weak recommendation?
Questions & Answers
QUESTION:
Problem 51P
A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that thcie is an 80 percent chance that she will get the job if she receives a strong recommendation, a 40 percent chance if she receives a moderately good recommendation, and a 10 percent chance if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate, and weak are .7, .2, and .1, respectively.
(a) How certain is she that she will receive the new job offer?
(b) Given that she does receive the offer, how likely should she feel that she received a strong recommendation? a moderate recommendation? a weak recommendation?
(c) Given that she does not receive the job offer, how likely should she feel that she received a strong recommendation? a moderate recommendation ? a weak recommendation?
ANSWER:
Step 1 of 4
Let us define the events as,
J = she gets the job offer,
NJ = she does not get the job offer,
S = she receives a strong recommendation,
M = she receives a moderate recommendation,
W = she receives a weak recommendation.
Also, we have:
P(J|S) = 0.8, P(J|M) = 0.4, P(J|W) = 0.1, P(NJ|S) = 0.2, P(NJ|M) = 0.6, P(NJ|W) = 0.9, And
P(S) = 0.7, P(M) = 0.2, P(W) = 0.1.
Here our goal is:
a). We need to check that how certain is she that she will receive the new job offer.
b). We need to check that how likely should she feel that she received a strong recommendation, a moderate recommendation, and a weak recommendation.
c). We need to check that how likely should she feel that she received a strong recommendation, a moderate recommendation, and a weak recommendation.