A company uses three different assembly lines- A1, A2 and A3 to manufacture a particular component. Of those manufactured by line A1, there are 5% that need rework to remedy a defect, whereas 8% of A2’s components need rework and 10% of A3’s need rework. Suppose that 50% of all components are produced by line A1, while 30% are produced by line A2 and 20% come from line A3. What is the probability that a randomly selected component:
1. came from line A1 and needed rework.
2. needed rework?
3. came from line A2, given that it needed rework.
4. came from line A3, and needed rework.
Answers
Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
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: p(r|a^1) = 0.05
a^2 = 0.08
a^3 = 0.10
a^1 = 0.50
a^2 = 0.30
a^3 = 0.10
Compute the probability that a randomly selected component needs rework as follows:
(0.05)*(0.50)+(0.08*0.30)+(0.10*0.20)
= 0.069
Compute the probability that a randomly selected component needs rework when it came from line A₁ as follows:
0.50*0.05/0.069=0.3623
Thus, the probability that a randomly selected component needs rework when it came from line A₁ is 0.3623.