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 0.93. 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? (Answer to four decimal places).
2. Suppose that the probability of having a particular disease is 0.07. Suppose that the probability of testing positive for the disease is 0.94 given that a person has the disease and 0.05 given that the person does not have the disease. Given that a person tests positive for the disease, what is the probability that they actually have the disease? (Answer to four decimal places).
3. Suppose that the probability that a customer plans to make a purchase is 0.28. Suppose that the probability of responding to an advertisement given that the customer plans to make a purchase is 0.61 and that the probability of responding to an advertisement given that a person does not plan to make a purchase is 0.13. Given that a person responds to the advertisement, what is the probability that they plan to make a purchase? (Answer to four decimal places).
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