Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that don't conform to specifications.

a) what is the probability that the inspector finds exactly one nonconforming part?
b) what is the probability that the inspector finds at least one nonconforming part?

Anyone able to explain this

Question

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that don't conform to specifications.

a) what is the probability that the inspector finds exactly one nonconforming part?
b) what is the probability that the inspector finds at least one nonconforming part?

Anyone able to explain this

kropot72 · Answer

$$P(1\ nonconforming)=3C1\times (\frac{1}{6})\times (\frac{5}{6})^{2}$$

australopithecus · Answer

how did you get that?

kropot72 · Answer

The binomial distribution is used to solve this question.