Wire manufactured by a company is tested for strength. The test gives a correct positive result with a probability of 0.85 when the wire is strong, but gives an incorrect positive result (false positive) with a probability of 0.04 when in fact the wire is not strong.If 98% of the wires are strong, and a wire chosen at random fails the test, what is the probability it really is not strong enough?

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ejigaboo8y · Accepted Answer

Events - Strong wire   P  (  S  ) Weak Wire   P  (      S    ′    ) Result   =  P  (  T  ) - true positive result  P  (  S  )  =  0.98  P  (      S    ′    )  =  0.02  P  (  T      |    S  )  =  0.85  P  (  T      |        S    ′    )  =  0.04  P  (  S      |    T  )  =  (  P  (  T      |    S  )  ×  P  (  S  )  )      /    [  (  P  (  T      |    S  )  ×  P  (  S  )  )  +  (  P  (  T      |        S    ′    )  ×  P  (      S    ′    )  )  ]  P  (  S      |    T  )  =  0.85  ×  0.98      /    (  0.85  ×  0.98  +  0.04  ×  0.02  )  =  0.8673      /    0.8681  =  0.9991  =  99.91  99.91  % times wires are strong when tested positiveFor wires tested strong and result is weak   =  1  −  P  (  S      |    T  )  =  1  −  0.99  =  0.01  =  1  % So, a wire chosen from suite of strong tested wire and comes out to be weak is   1  %

Wire manufactured by a company is tested for strength. The test gives a correct positive result with

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