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

If a randomly selected component needs rework, the probability that it came from line A1 is 36.23%.

Given that a company uses three different assembly lines- A1, A2, and A3- to manufacture a particular component, and of those manufactured by line A1, 5% need rework to remedy a defect, whereas 8% of A2's components need rework and 10% of A3's need rework, supposing that 50% of all components are produced by Line A1, 30% are produced by line A2, and 20% come from line A3, if a randomly selected component needs rework, to determine what is the probability that it came from line A1 the following calculation must be performed:

Therefore, if a randomly selected component needs rework, the probability that it came from line A1 is 36.23%.

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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 R as the event that a component needs rework.

It is given that:

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

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

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