Question

b. A company has two plants to manufacture scootors.Plant A manufactures 70% of scooters
and plant B manufactures 30% .At Plant A ,80% scooters are rated standard quality and
plant B ,90% of scooters rated standard quality. A scooter is picked up at random and
found to be of standard quality.
a. What is the chance that it ha come from Plant A

Answer 1

72 √chance

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that  

• E₁ be the plant A manufacture the scooter

• E₂ be the plant B manufacturing the scooter.

• E the scooter is of standard quality.

Further given that,

$\red{\rm :\longmapsto\:P(E_1) = \dfrac{70}{100} \: }$

$\red{\rm :\longmapsto\:P(E_2) = \dfrac{30}{100} \: }$

$\red{\rm :\longmapsto\:P(E | E_1) = \dfrac{80}{100}}$

$\red{\rm :\longmapsto\:P(E | E_2) = \dfrac{90}{100}}$

Now, by using Baye's Theorem we get,

Then, the required probability that the scooter is of standard quality and manufactured by plant A is

$\red{\rm :\longmapsto\:P(E_1 | E)}$

$\red{\rm \:  =  \: \sf \dfrac{P(E_1) . P(E | E_1)}{P(E_1) . P(E | E_1) + P(E_2) . P(E | E_2)}}$

$\red{\rm \:  =  \: \dfrac{\dfrac{70}{100} \times \dfrac{80}{100} }{\dfrac{70}{100} \times \dfrac{80}{100} + \dfrac{30}{100} \times \dfrac{90}{100} }}$

$\red{\rm \:  =  \: \dfrac{5600}{5600 + 2700}}$

$\red{\rm \:  =  \: \dfrac{5600}{8300}}$

$\red{\rm \:  =  \: \dfrac{56}{83}}$