1.

A company manufactures scooters at two plants, A and B. Plant A produces 80% and plant B produces 20% of the total product. 85% of the scooters produced at plant A and 65% of the scooters produced at plant B are of standard quality. A scooter produced by the company is selected at random and it is found to be of standard quality. What is the probability that it was manufactured at plant A?

Answer»

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Solution :Let `E_1`=EVENT that the selected scooter is produced at PLANT A, and
`E_2` =event that the selected scooter is produced at plant B.
Then, `P(E_1)=80/100=4/5andP(E_2)=20/100=1/5`.
Let E be the event of choosing a scooter which is of standrad quality.
Then, `P(E//E_1)=85/100=17/20,and P(E//E_2)=65/100=13/20`
PROBABILITYTHAT the selected scooter was produced at plant A, given that it is of
Standard quality
`=P(E_1//E)`
`=(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`


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