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A company has two plants to manufacture scooters. Plant I manufactures 70% of the scooters and plant II manufactures 30%. At plant I, 80% of the scooters are rated as of standard quality and at plant II, 90% of the scooters are rated as of standard quality. A scooter is chosen at random and is found to be of standard quality. What is the probability that it has come from plant II?

Asked by Topperlearning User 20th August 2016, 12:00 AM
Answered by Expert
Answer:

E subscript 1 equals p l a n t space text I  end text m a n u f a c t u r e s space s c o o t e r
E subscript 2 equals p l a n t space text II  end text m a n u f a c t u r e s space s c o o t e r
A equals s c o o t e r space i s space o f space s tan d a r d space q u a l i t y
P left parenthesis E subscript 1 right parenthesis equals 70 over 100 space P left parenthesis E subscript 2 right parenthesis equals 30 over 100 space P left parenthesis A divided by E subscript 1 right parenthesis equals 80 over 100 space P left parenthesis A divided by E subscript 2 right parenthesis equals 90 over 100
B y space B a y e apostrophe s space T h e o r e m
P left parenthesis E subscript 2 divided by A right parenthesis equals fraction numerator P left parenthesis E subscript 2 right parenthesis P left parenthesis A divided by E subscript 2 right parenthesis over denominator P left parenthesis E subscript 2 right parenthesis P left parenthesis A divided by E subscript 2 right parenthesis plus P left parenthesis E subscript 1 right parenthesis P left parenthesis A divided by E subscript 1 right parenthesis end fraction equals fraction numerator 27 over denominator 27 plus 56 end fraction equals 27 over 83

Answered by Expert 20th August 2016, 2:00 AM
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