1. Suppose that the probability of getting a job offer (from a specific company)

Question

1. Suppose that the probability of getting a job offer (from a specific company) is 0.14. Suppose that we observe empirically that given that an applicant for the job was in fact offered a job, the probability of an on campus interview was 0.92. Also, we observe empirically that given the group that were not offered a job the probability of an on campus interview was of 0.09.  Given that a person got a campus interview, what is the probability that they get a job offer?

2. T/F? Union implies an or condition. That is, a member of the union of sets A and B is any member of set A or set Bor a member of both A and B.

3. T/F?  Intersection implies an and condition. For example, a member of the intersection of sets A and Bis any member of setsAandB.

4. Suppose that the probability that a customer plans to make a purchase is 0.34. Suppose that the probability of responding to an advertisement given that the customer plans to make a purchase is 0.63 and that the probability of responding to an advertisement given that a person does not plan to make a purchase is 0.12.  Given that a person responds to the advertisement, what is the probability that they plan to make a purchase?

Explanation / Answer

1)probability of person got a campus interview =P(got a job offer and campus interview +does not get a job offer and campus interview) =0.14*0.92+(1-0.14)*0.09=0.2062

hence the probability that they get a job offer given campus interview  

=P(got a job offer and campus interview)/P(campus interview) =0.14*0.92/0.2062=0.6246

2) true

3) true

4)

probability that person responds to the advertisement =P(plan to purchase and responds+did not plan and responds) =0.34*0.63+(1-0.34)*0.12=0.2934

hence probability that they plan to make a purchase given responded

=P(plan to purchase and responds)/.P(responds) =0.34*0.63/0.2934=0.7301

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