The management of a company finds that 30% of the administrative assistants hire
ID: 2874377 • Letter: T
Question
The management of a company finds that 30% of the administrative assistants hired are unsatisfactory. The personnel director is instructed to devise a test that twill improve the situation. One hundred employed administrative assistants are chosen at random and are given the newly constructed test. Out of these. 90% of the satisfactory administrative assistants pass the test and 20% of the unsatisfactory administrative assistants pass. Based on these results, if a person applies for a job, takes the test, and passes it, what is the probability that he or she is a satisfactory administrative assistant? If the applicant fails the test, what is the probability that he or she is a satisfactory administrative assistant?
Explanation / Answer
let probabilty of satisfactory assistnat =P(S) =0.7
and that of passing the test =P(P)=P(S)*P(P|S)+P(U)*P(P|U)=0.7*0.9+0.3*0.2=0.69
1)hence probability that he or she is a satisfactory administrative assistant; given passess the test
=P(S)*P(P|S/P(P) =0.7*0.9/0.69 =0.913043
2)probabilty of failinjg the test =P(F) =P(S)*P(F|S)+P(U)*P(F|U)=0.7*0.1+0.3*0.8=0.31
hence probability that he or she is a satisfactory administrative assistant; given failed the test
=P(S)*P(F|S)/P(F)=0.7*0.1/0.31=0.225806
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