Question

(1 point) 4. A worker has asked her supervisor for a letter of recommendation for a new job. She estimates that there is an 80 percent probability that she will get the job if she receives a strong recommendation, a 0.40 probability if she receives a moderately good recommendation, and a 10% probability is she receives a weak recommendation. She urther estimates that the probabilities that the recommendation will be strong, moderate, or weak are 0.7, 0.2, and 0.1 respectively. (a) How certain is she to receive the new job offer? I(use at least four digits after the decimal if rounding...) (b) If she receives the job offer, what is the probability that she received a moderate recommendation? 掇 ( use at least four digits after the decimal if rounding ) (c) If she does not receive the job offer, what is the probability that she received a strong recommendation? ( use at least four digits after the decimal if rounding )

Answer 1

a)

P(new job) = P(high recommendation)*P(job|high recommendation)+P(moderate recommendation)*P(job|high recommendation)+P(low recommendation)*P(low|high recommendation)=0.80*0.7+0.40*0.2+0.10*0.1=0.65

b)

P(moderate|job) = 0.40*0.2/0.65=0.1231

c) P(no job) = 1-0.65 = 0.35

P(strong recommendation| no job ) = P(strong recommendation and no job)/P(no job) = 0.20*0.7/0.35 = 0.4