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elena-s [515]
2 years ago
6

A company uses three different assembly lines- A1, A2, and A3- to manufacture a particular component. Of thosemanufactured by li

ne A1, 5% need rework to remedy a defect, whereas8% of A2's components need rework and 10% of A3's need rework.Suppose that 50% of all components are produced by Line A1, 30% areproduced by line A2, and 20% come from line A3. if a randomlyselected component needs rework, what is the probability that itcame from line A1?
Mathematics
1 answer:
hammer [34]2 years ago
6 0

Answer:

The probability that a randomly selected component needs rework when it came from line A₁ is 0.3623.

Step-by-step explanation:

The three different assembly lines are: A₁, A₂ and A₃.

Denote <em>R</em> as the event that a component needs rework.

It is given that:

P (R|A_{1})=0.05\\P (R|A_{2})=0.08\\P (R|A_{3})=0.10\\P (A_{1})=0.50\\P (A_{2})=0.30\\P (A_{3})=0.20

Compute the probability that a randomly selected component needs rework as follows:

P(R)=P(R|A_{1})P(A_{1})+P(R|A_{2})P(A_{2})+P(R|A_{3})P(A_{3})\\=(0.05\times0.50)+(0.08\times0.30)+(0.10\times0.20)\\=0.069

Compute the probability that a randomly selected component needs rework when it came from line A₁ as follows:

P (A_{1}|R)=\frac{P(R|A_{1})P(A_{1})}{P(R)}=\frac{0.05\times0.50}{0.069}  =0.3623

Thus, the probability that a randomly selected component needs rework when it came from line A₁ is 0.3623.

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