Applicants who wish to be admitted to a certain professional school in a large u

Question

Applicants who wish to be admitted to a certain professional school in a large university are required to take a screening test devised by an educational testing service. From past results, the testing service has established that 80% of all applicants are eligible for admission and that 88% of those who are eligible for admission pass the exam, whereas 12% of those who are ineligible for admission pass the exam. (Round your answers to three decimal places.)

(a) What is the probability that an applicant for admission passed the exam?

(b) What is the probability that an applicant for admission who passed the exam was actually ineligible?

Explanation / Answer

The testing service has established that 80% of all applicants are eligible for admission and that 88% of those who are eligible for admission pass the exam, whereas 12% of those who are ineligible for admission pass the exam

a. P(  an applicant for admission passed the exam) = .80*.88+.20*.12 = .728

b. P(probability that an applicant for admission who passed the exam was actually ineligible) = (.20*.12)/.728 = .0329

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