Question

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 15 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 3 part(s) from among the 15 at random. Three cavities are affected by a temperature malfunction that results in parts that do not conform to specifications. Round your answers to four decimal places. (a) What is the probability that the inspector finds exactly one nonconforming part

Answer 1

0.006593

Explanation:

Let K be the number of possibilities that 3 parts can be chosen randomly from among 15.

K is the combination of 15 taken 3 at a time

`\binom{15}{3}=(15!)/(3!(15-3)!)=(15!)/(3!12!)=(15.14.13)/(6)=455`

Of this 455 possibilities of choosing 3 parts, only 3 can have exactly one nonconforming part.

So the probability of finding three parts with exactly one defective is

`(3)/(455)=0.006593\approx 0.65\%`