An article compared the results of magnetic resonance imaging (MRI) evaluation w
ID: 3306654 • Letter: A
Question
An article compared the results of magnetic resonance imaging (MRI) evaluation with arthroscopic surgical evaluation of cartilage tears at two sites in the knees of 35 patients. The 2 × 35 = 70 examinations produced the classifications shown in the table. Actual tears were confirmed by arthroscopic surgical examination. (Enter exact numbers as integers, fractions, or decimals.) Tears No Tears Total MRI Positive 27 0 27 MRI Negative 2 41 43 Total 29 41 70
(a) What is the probability that a site selected at random has a tear and has been identified as a tear by MRI?
(b) What is the probability that a site selected at random has no tear and has been identified as having a tear?
(c) What is the probability that a site selected at random has a tear and has not been identified by MRI?
(d) What is the probability of a positive MRI, given that there is a tear?
(e) What is the probability of a false negative—that is, a negative MRI, given that there is a tear?
Explanation / Answer
MRI Positive MRI Negative Total
Tears 27 0 27
No Tears 2 41 43
Total 29 41 70
(a) What is the probability that a site selected at random has a tear and has been identified as a tear by MRI?
required probability=P(Tears|MRI positive ) = P(Tears and MRI positive)/P(MRI positive)=(27/70)/(29/70)=27/29
(b) What is the probability that a site selected at random has no tear and has been identified as having a tear?
required probability=2/29
(c) What is the probability that a site selected at random has a tear and has not been identified by MRI?
required probability=0
(d) What is the probability of a positive MRI, given that there is a tear?
=27/70
(e) What is the probability of a false negative—that is, a negative MRI, given that there is a tear?
required prbability=2/70
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