<u>The required </u><u>probability </u><u>that the inspector finds exactly one nonconforming part </u><u>0.4352 .</u>
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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