question

Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as Xray computed tomography, ultrasonics, and acoustic emission. Recently, NDE was used to detect defects in steel castings. Assume that the probability that NDE detects a "hit" (i.e., predicts a defect in a steel casting) when, in fact, a defect exists is 0.95. (This is oen called the probability ofdetection.) Assume also that the probability that NDE detects a "hit" when, in fact, no defect exists is 0.008. (This is called the probability of a false call.) Past experience has shown that a defect occurs once in every 100 steel castings. If NDE detects a "hit" for a particular steel casting, what is the probability that an actual defect exists? The probability that an actual defect exists is (Round to three decimal places as needed.)