Question

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 11 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 1 part(s) from among the 11 at random. Three cavities are affected by a temperature malfunction that results in parts that do not 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?

Answer 1

Answer:

a) 0.27 %                                  b) 0.27%

Explanation:

a) The inspector can choose 1 part from 11 parts in  11C1 ways. These are total number of mutually exclusive events.

Now three cavities are effected by temperature Malfunction that results in the parts that do not conform to specifications. To obtain exactly 1 non conforming part the inspector have to choose from one of the three cavities that are effected by temperature. This can be done in 3C1 ways.

Probability that inspector finds out exactly 1 non conforming part is,

Probability = $\frac{3C1}{11C1}$  

         Probability  =    $\frac{\frac{3!}{1!(3-1)!} }{\frac{11!}{1!(11-1)!} }$     = 3 / 11

                            =  0.27 %

b)  As the inspector is choosing only 1 part for inspection so the probability to find exactly 1 non conforming part is same as the probability to find at least 1 non conforming part.

    So the probability is 0.27 %.