Applicants who wish to be admitted to a certain professional school in a large u
ID: 3119718 • Letter: A
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 70% of all applicants are eligible for admission and that 87% of those who are eligible for admission pass the exam, whereas 15% 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
87% of 70% = 60.9%
15% of 30% = 4.5%
Therefore (60.9 + 4.5)% = 65.4% of all applicants pass the exam, i.e. probability = 0.654
Out of 65.4% of applicants who pass the exam, 4.5% are ineligible,
so the probability = 4.5 / 65.4 = 0.0688
To make it easier, think in terms of numbers. Say that there are 1000 applicants. Then you are given the following data :
. . . . . . . . . . . . . Eligible. . . . . . . . Not eligible
. . . . . . . . . . . . .-----------. . . . . . .-----------------
. . Pass. . . . . . .70% x 700. . . . . . 15% x 300
. . Fail . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .Totals. . . . . . . . 700. . . . . . . . . . . . 300.
It should be simple now to complete the rest of it,
. . . . . . . . . . . . . Eligible. . . . . . . . Not eligible
. . . . . . . . . . . . .-----------. . . . . . .-----------------
. . Pass. . . . . . . . 490. . . . . . . . . . . . . 45
. . Fail . . . . . . . . . .210 . . . . . . . . . . . . 255
. .Totals. . . . . . . . 700. . . . . . . . . . . . .300
So (a) is (490 + 45) / 1000 =0.535
And (b) is 28 / (28 + 760)=45/(45+700)
=0.060
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