5) When a serious defect with a cell phone is discovered, a detailed investigarr

Question

5) When a serious defect with a cell phone is discovered, a detailed investigarrectly identified is the cause is conducted. The probability that a defect due to a programing error 0.90. The probability that a defect that is not due to aprogram inge%ofall cell phone identified as being due to a programming error is 0.20. Su defects are due to programming errors. Determine the probability that a cell phone defect is due to a programming error given that it has been diagnosed as due to a programming error. correctly error is incorrectly

Explanation / Answer

P(defects due to programming error) = 0.25

P(correctly identified | defects due to programming error) = 0.9

P(incorrectly identified | defects not due to programming error) = 0.2

P(correctly identified | defects not due to programming error) = 1 - 0.2 = 0.8

P(correctly identified) = P(correctly identified | defects due to programming error) * P(defects due to programming error) + P(correctly identified | defects not due to programming error) * P(defects not due to programming error)

                            = 0.9 * 0.25 + 0.8 * 0.75

                            = 0.825

P(defects due to programming error | correctly identified) = P(correctly identified | defects due to programming error) * P(defects due to programming error) / P(correctly identified)

                                             = 0.9 * 0.25 / 0.825

                                             = 0.2727

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