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In: Statistics and Probability

Quality assurance department of software house reveals that 6.5% of programming code contain logical errors. Quality...

Quality assurance department of software house reveals that 6.5% of programming code contain logical errors. Quality check software is developed to analyze code and in a test, identifies the error in 90% of the code with errors and 5% of those without. If code is marked by the program as possibly having a logical error, what is the probability that the code DOES have an error?

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Expert Solution

P[ programming code contain logical errors ] = 6.5% = 0.065

P[ programming code does not contain logical errors ] = 1 - P[ programming code contain logical errors ]

P[ programming code does not contain logical errors ] = 1 - 0.065

P[ programming code does not contain logical errors ] = 0.935

P[ Quality check software identifies the error | programming code contain logical errors ] = 90% = 0.9

P[ Quality check software identifies the error | programming code does not contain logical errors ] = 5% = 0.05

P[ Quality check software identifies the error ] = P[ Quality check software identifies the error | programming code contain logical errors ]*P[ programming code contain logical errors ] + P[ Quality check software identifies the error | programming code does not contain logical errors ]*P[ programming code does not contain logical errors ]

P[ Quality check software identifies the error ] = 0.9*0.065 + 0.05*0.935

P[ Quality check software identifies the error ] = 0.0585 + 0.04675

P[ Quality check software identifies the error ] = 0.10525

P[ programming code does not contain logical errors | Quality check software identifies the error ] = P[ Quality check software identifies the error | programming code does not contain logical errors ]*P[ programming code does not contain logical errors ] / P[ Quality check software identifies the error ]

P[ programming code does not contain logical errors | Quality check software identifies the error ] =  0.05*0.935 / 0.10525

P[ programming code does not contain logical errors | Quality check software identifies the error ] = 0.04675/ 0.10525

P[ programming code does not contain logical errors | Quality check software identifies the error ] = 0.4442

P[ programming code does not contain logical errors | Quality check software identifies the error ] = 44.42%

orchestra answered 1 year ago
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