Plastic parts produced by an injectionmolding operation arec

Plastic parts produced by an injection-molding operation arechecked for conformance to specifications. Each tool contains 12cavities in which parts are produced, and these parts fall into aconveyor when the press opens. An inspector chooses 3 parts fromamong the 12 at random. Two cavities are affected by a temperaturemalfunction that results in parts that do not conform tospecifications. 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? c. what is the probability that the inspector finds at least two nonconforming part?

Solution

Prob for defective = 2/12 = 0.1667

Each is independent and there are two outcomes

X - no of defectives is binomial (12, 0.1667)

a) P(X=1) = 0.2691

b) P(X>=1) = 1-P(X=0) = 1-0.1121

= 0.8879

c) P(X>=2) = P(X=2 or 3)

= 0.2961+0.1974

= 0.4935