Question
In: Statistics and Probability
Cars are being produced by two factories, but factory I produces twice as many cars as...
Cars are being produced by two factories, but factory I produces
twice as many cars as factory II in a given time. Factory I is
known to produce 2% defectives and factory II produces 1%
defectives. A car is examined and found to be not defective. What
is the probability that it came from factory 1?
Solutions
Expert Solution
P[ car produced in factory I ] = 2/3
P[ car produced in factory II ] = 1/3
P[ defective | factory I ] = 2% = 0.02
P[ non defective | factor I ] = 1 - P[ defective | factory I ]
P[ non defective | factor I ] = 1 - 0.02
P[ non defective | factor I ] = 0.98
P[ defective | factory II ] = 1% = 0.01
P[ non defective | factor II ] = 1 - P[ defective | factory II ]
P[ non defective | factor II ] = 1 - 0.01
P[ non defective | factor II ] = 0.99
P[ non defective ] = P[ non defective | factor II ]*P[ car produced in factory II ] + P[ non defective | factor I ]*P[ car produced in factory ]
P[ non defective ] = 0.99*(1/3) + 0.98*(2/3)
P[ non defective ] = ( 0.99 + 1.96 )/3
P[ non defective ] = 0.983
We need to find
P[ factor I | non defective ] = P[ non defective | factor I ]*P[ car produced in factory ] / P[ non defective ]
P[ factor I | non defective ] = 0.98*(2/3) / 0.983
P[ factor I | non defective ] = 0.653/0.983
P[ factor I | non defective ] = 0.6644
orchestra answered 2 years agoRelated Solutions
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