Question

A company has two plants which manufacture scooters.Plant i manufactures 70% of the scooters while plant ii manufactures 30% of the scooters.At plant i ,85 out of 100 scooters are rated as being of standard quality,while at plant ii only 65 out of 100 scooters are rated as being of standard quality.If a scooter is of standard quality,what is the probability that it came from plant i?

Answer 1

Q)

 

A company has two plants which manufacture scooters.Plant I manufactures 80% of the scooters while Plant II manufactures 20% of the scooters.At plant I ,85 out of 100 scooters are rated as being of standard quality,while at Plant II only 65 out of 100 scooters are rated as being of standard quality.If a scooter is of standard quality,what is the probability that it came from Plant?



A)

 

Let S be the event that  scooter is standard quality 

A be the event that scooter is manufacture from plant 1

B be the event that scooter is manufacture from plant 2 

p(A)=0.80

P(B)=0.20

P(A/S)=85/100=0.85

P(B/S)=65/100=0.65

By the Bay's theorem

P(S/A)=(P(A)/P(A/S))/((P(A)/P(A/S))+(P(B)/P(B/S)))

=(0.80*0.85)/((0.80*0.85)+(0.80*0.85))

=0.68/0.81

=0.84

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