Question

Parts coming off an assembly line in a manufacturing process are checked by one of three quality assurance technicians. Technician 1 receives 40% of parts, Technician 2 receives 25% of parts, and Technician 3 receives the remaining parts.Occasionally, even the best trained technicians can let a defective part slip through. Of the parts they receive, Technician 1 misses 5% of the parts that are defective. Technician 2 misses 7% of the parts that are defective. Technician 3 misses 3% of the parts that are defective.

A) construct and label the tree diagram for this problem

B) What is the probability that a defective part from the assembly line gets throughquality assurance without being caught?

C) SUppose a defective part was missed by the technicians. What is the probabilitythat this defective part was missed by Technician 2 ?

Answer 1

Answer:-

Given That:-

Parts coming off an assembly line in a manufacturing process are checked by one of three quality assurance technicians. Technician 1 receives 40% of parts, Technician 2 receives 25% of parts, and Technician 3 receives the remaining parts.Occasionally, even the best trained technicians can let a defective part slip through. Of the parts they receive, Technician 1 misses 5% of the parts that are defective. Technician 2 misses 7% of the parts that are defective. Technician 3 misses 3% of the parts that are defective.

Given,

Let denote the event that the technician 1, techinician 2 and technician 3 receives the parts.

p() = 4/100

= 0.40

p() = 25/100

= 0.25

p() = 1 - p() - p()

= 1 - 0.40 - 0.25

= 0.35

Let A denote the event that a defective part from the assembly line gets through quality assurance without being caught.

= 0.05

= 0.40 * 0.05 + 0.25 * 0.07 + 0.35 * 0.03

= 0.048

= (0.25 * 0.07) / 0.048

= 0.36458

A) construct and label the tree diagram for this problem

B) What is the probability that a defective part from the assembly line gets throughquality assurance without being caught?

The probbaility that a defective part from the assembly gets through quality assurance without being caught = P(A)

= 0.048

C) SUppose a defective part was missed by the technicians. What is the probabilitythat this defective part was missed by Technician 2 ?

The Probability that this defective part was missed by technician 2 =

= 0.36458

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