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?

(B)What is the probability that the inspector finds at least one nonconforming part?

Answer 1

Answer:

(A) 0.006593 or 0.6593%

(B) 0.01538 or 1.538%

Step-by-step explanation:

The total number of possibilities to pick 3 parts out of 15 possible parts is given by the following combination:

$n=\frac{15!}{(15-3)!3!}=\frac{15*14*13}{3*2*1}\\n=455\ ways$

(A) There are only three possibilities for which the inspector finds exactly one nonconforming part (NCC, CNC, CCN). Therefore, the probability is:

$P(N=1) = \frac{3}{455}=0.006593 =0.6593\%$

(B) There are three possibilities  for which the inspector finds exactly one nonconforming part, three possibilities for two nonconforming parts (NNC, CNN, NCN), and one possibility for all nonconforming parts (NNN). The probability that the inspector finds at least one nonconforming part is:

$P(N>0) =P(N=1)+P(N=2)+P(N=3) \\P(N>0) = \frac{3}{455}+ \frac{3}{455}+ \frac{1}{455}\\P(N>0) =0.01538 =1.538\%$