Question

algebra.com 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 do not conform to specifications.

Answer 1

The required probability that the  inspector finds exactly one nonconforming part  0.4352 .

What does probability mean in math?

The study of probability is a field of mathematics that determines the probability of an event occurring, which is represented by a number between 1 and 0.

The inspector has a total of 15 pieces from which to choose 3 in 15 different ways. These are all of the instances that are mutually exclusive, mutually exhaustive, and both likely.

A temperature problem now affects three cavities, producing parts that don't meet specifications. It indicates that the inspector selects one of the three cavities that are impacted by temperature malfunction in order to obtain precisely one nonconforming element.

This can be done in (3 1) ways . Now to obtain two non defective parts from two cavities it implies that we have to select two cavities from the remaining 12 properly functioning cavities which can be done in ( 12 2 ) ways .

So the required probability that the  inspector finds exactly one nonconforming part

     =  ( 12 2 ) × (3 1 ) / ( 15 3 )

     = 0.4352

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