Question

A worker has asked her supervisor for a confidential letter of recommendation for a new job. She estimates that there is an 80% chance that she will get the job if she receives a strong recommendation, a 40% chance if she receives a moderately good recommendation, and a 10% if she receives a weak recommendation. She further estimates that the probabilities that the recommendation will be strong, moderate and weak are 0.6, 0.3 and 0.1 respectively. Given that she fails to get the job, what is the probability that she received a weak recommendation?

Answer 1

P(   strong   ) =    0.6
P(   moderate   ) =    0.3
P(    weak   ) =    0.1
total=           1
          
P(   do not get job   | strong)= 1 - 0.8 = 0.2
P(   do not get job   | moderate)= 1-0.4 = 0.6
P(   do not get job   | weak)= 1-0.1 = 0.9

P(do not get job) = P(strong) * P(do not get job| strong) + P(moderate) *P(do not get job| moderate) + P( weak)*P(do not get job| weak) =                                    0.6*0.2+0.3*0.6+0.1*0.9=               0.39  

P( weak| do not get job) = P( weak)*P(do not get job| weak)/P(do not get job)=               0.1*0.9/0.39=       0.2308 (answer)