Question

Suppose that the probability of getting a job offer (from a specific company) is 0.17. 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 0.07. Given that a person got a campus interview, what is the probability that they get a job offer?

Answer 1

P (X | CI) = 0.7313

Explanation:

X = event of getting a job

CI = Campus interview

P (X | CI) = p ( CI ∩ X) / P ( CI ) = P( CI | X)P(X) / P( CI | X)P(X) + P( CI | X')P(X')

P (X | CI) = 0.93 * 0.17 / 0.93 * 0.17 + 0.07 * (1 - 0.17)

P (X | CI) = 0.93 * 0.17 / 0.93 * 0.17 + 0.07 * 0.83

P (X | CI) = 0.1581 / 0.1581 + 0.0581

P (X | CI) = 0.1581 / 0.2162

P (X | CI) = 0.73126735

P (X | CI) = 0.7313