Aluminum usage in automobiles has been climbing steadily. As recently as 1990, there were no aluminum-structured passenger cars in production anywhere in the world, but by 1997, there were seven of them, including the Audi A8. With weight savings of up to 47% over steel vehicles, such cars use less fuel, create less pollution, and are recyclable. Aluminum pistons are also used in automotive internal combustion engines. Aluminum pistons are manufactured through casting because of its capability to produce near-net shaped parts at the required production rates. However, with poorly designed molds, under-fills or excess porosity can cause parts to be rejected. In a process that manufactures certain aluminum pistons, the probability that a piston has an under-fill defect is 0.05, the probability that a piston has a porosity defect is 0.04, and the probability that a piston has both defects is 0.01. What is the probability that a randomly chosen piston has a defect?

Question

Mathematics

Kobe

29 April, 10:49

Aluminum usage in automobiles has been climbing steadily. As recently as 1990, there were no aluminum-structured passenger cars in production anywhere in the world, but by 1997, there were seven of them, including the Audi A8. With weight savings of up to 47% over steel vehicles, such cars use less fuel, create less pollution, and are recyclable. Aluminum pistons are also used in automotive internal combustion engines. Aluminum pistons are manufactured through casting because of its capability to produce near-net shaped parts at the required production rates. However, with poorly designed molds, under-fills or excess porosity can cause parts to be rejected. In a process that manufactures certain aluminum pistons, the probability that a piston has an under-fill defect is 0.05, the probability that a piston has a porosity defect is 0.04, and the probability that a piston has both defects is 0.01. What is the probability that a randomly chosen piston has a defect?

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Answers (1)

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Duncan Rivers · Answer 1

P (A U B) = 0.08

Step-by-step explanation:

1. Let:

P (A) as the probability that a psiton has an under-fill defect

P (B) as the probability that a pistón has a porosity defect

P (A ∩ B) the probability of having both defectos

Then:

P (A) = 0.05

P (B) = 0.04

P (A ∩ B) = 0.01

2. The probability that a randomly chosen piston has a defect could be calcularse as the union of the probability of choosing a piston with am under-fill defect and one with porosity defect.

That Is P (A U B)

Aplying the probability properties we have:

P (A U B) = P (A) + P (B) - P (A ∩ B)

Replacing the probabilities:

P (A U B) = 0.05+0.04-0.01

P (A U B) = 0.08