Question

An article studied the accuracy of MRIs (magnetic resonance imaging) in detecting cartilage tears at two sites in the knees of 35 patients. The 2 x 35 - 70 examinations produced the classifications shown in the table. Actual tears were confirmed by arthroscopic surgical examination (Enter your probabilities as fractions.) Tears MRI Positive 25 MRI Negative 2 Total 27 No Tears 0 4 3 43 Total 25 45 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?

Answer 1

solution Here from the given data Tears No Tears I Total MR positive 25 o 25. MRI negative z uz us Total 127 43 70 a) p (Tear & positive) = 25 = 0.357) 6) p (no tear & psutive ) = 0 = 0 op (tear $ negative) = z = 0.0286 d) p (posutive/ tear) = 25 2 = 0.9259 e) plnegative / tear) = = 6-074)