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?

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?

anonymous · Answer

a

kropot72 · Answer

a)$$P(exactly\ 1\ nonconforming)=\frac{2C1\times10C2}{12C3}=you\ can\ calculate$$
b)$$P(0\ nonconforming)=\frac{2C0\times10C3}{12C3}$$
When you have calculated the probability of zero nonconforming parts, subtract that value of probability from 1. This will give the probability of finding at least one nonconforming part in the sample of three parts.