Question

A part is randomly selected at random during a quality assurance test and is found to be defective. Calculate the probability that it was supplied by supplier B

Answer 1

Answer:

Answer according to your question.

Answer 2

Total problem

Quality assurance is an important aspect of any business. This case study is based on Lyman Limited, a company that manufactures and sells office furniture. They obtain parts (hinges, chair wheels, etc.) from three different suppliers, A, B, and C. Past experience has shown that 20% of the parts are supplied by A, 50% are supplied by B and the rest are supplied by C. It is also known that 10% of the parts supplied by A are defects, 8% of the parts from B are defect and 6% of the parts from C are defect.

Question 1:

A part is randomly selected during a quality assurance test and is found to be defective. Calculate the probability that it was supplier B.

Answer:

A = parts from A

P(A) = 20 % = 0.2

B = parts from B

P(B) = 50% = 0.5

C = Parts from C

P(C) = (1-P(A)-P(B)) = 1 -0.2 -0.5 =0.3

P(came from A and defective) = 0.1

P(came from B and defective) = 0.08

P(came from C and defective) = 0.06

P(part was supplied by supplier B) =

$=\frac{0.5 \times 0.08}{0.2 \times 0.1+0.5 \times 0.08+0.3 \times 0.06}\\=0.5128$

The probability that it was supplier B was 0.5128.