A company has tow plant to manufacture bicycles. The first plant manufactures 60% of the bicycles and the second plant 40%. Out of that 80% of the bicycles are rated of standard quality at the first plant and 90% of standard quality at the second plant. A bicycle is picked up at random and found to be standard quality. Find the probability that it comes from the second plant.

Explanation

A company has `2` plant to manufacture bicycles.
The first plant
manufactures `60%` of the bicycles and also the second plant `40%`.
Out of that `80%` of
the bicycles are rated of standard quality at the primary plant and
`90%` of
standard quality at the second plant.
Let `E_1`be the event the cycle is from the primary plant.
Let `E_2`be the event the cycle is from the second plant.
Let `A` be the event the cycle is standard.
`p(E_1)=0.6` and `p(E_2)=0.4`
`P(A/E_1)=0.8 and p(A/E_2)=0.9`
From Bayer theorem,
`p(E_2/A)=(p(E_2)xxp(A/E_2))/(p(E_1)xxp(A/E_1)+p(E_2)xxp(A/E_2)`
`=((0.4)xx(0.9))/((0.6)(0.8)+(0.4)(0.9))`
`=0.36/0.84`
`=3/7`