Analysis of historical data shows the probability a machine tool your company produces will fail when installed in a customer's factory is 0.04. Your quality assurance department utilizes sophisticated testing and diagnostic equipment to determine whether a machine tool you produce will function once it is installed in a customer's factory. If the machine tool would function when installed, the probability that quality assurance department testing would indicate the machine tool will fail when installed is 0.08. If the machine tool will fail when installed, the probability that quality assurance testing will indicate the machine tool will fail is 0.97.

What is the probability that machine tool will function when installed given the quality assurance testing indicates the machine tool will function?

Question

Mathematics

Paris Short

17 May, 01:14

Analysis of historical data shows the probability a machine tool your company produces will fail when installed in a customer's factory is 0.04. Your quality assurance department utilizes sophisticated testing and diagnostic equipment to determine whether a machine tool you produce will function once it is installed in a customer's factory. If the machine tool would function when installed, the probability that quality assurance department testing would indicate the machine tool will fail when installed is 0.08. If the machine tool will fail when installed, the probability that quality assurance testing will indicate the machine tool will fail is 0.97.

What is the probability that machine tool will function when installed given the quality assurance testing indicates the machine tool will function?

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Answers (1)

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Danny Bowen · Answer 1

0.9986

Step-by-step explanation:

Prob (Machine tool actually fails) = 0.04 So, Prob (Machine tool actually functions) = 1 - 0.04 = 0.96 Prob (functional machine tool claimed fail) = 0.08 So, Prob (functional machine tool claimed functional) = 1 - 0.08 = 0.92 Prob (fail machine tool claimed fail) = 0.97 So, Prob (fail machine tool claimed functional) = 1 - 0.97 = 0.03

Prob A: P [Machine tool indicated (claimed) functional] : - Functional machine tool or fail machine tool claimed functional = (0.96) (0.92) + (0.04) (0.03) = 0.8844

Prob B: P [Machine tool actually function when passed by QAs] = (0.96) (0.92) = 0.8832

Prob (A given B) = P (A & B) / P (A)

= 0.8832 / 0.8844 = 0.9986