Problem 1. (6 Points) A manufacturer receives defective products returned by cus

Question

Problem 1. (6 Points) A manufacturer receives defective products returned by customers, and upon analysis of the type of defects found in the returned products finds that: #55% of the returned products had faulty assembly, +45% of the returned products had failed components, and #70% of the returned products had at least one of the above two types of defects. For a randomly selected returned product, find the following: (a) The probability that it had neither faulty assembly nor failed components (i.e., had some other type of defect). (b) The probability that it had both a faulty assembly as well as failed components. (c) The probability that it has an assembly fault, but no failed components.

Explanation / Answer

Let FA = faulty assembly, FC = failed components.

P(FA) = 0.55, P(FC) = 0.45

P(FA or FC) = 0.70

a)

Probability of neither faulty assembly nor failed components = P( FA or FC)'

= 1 - P( FA or FC)

= 1 - 0.70

= 0.30

Probability of neither faulty assembly nor failed components = 0.30

b)

We have to calculate P(FA and FC) = ?

Using addition rule, P(A or B) = P(A) + P(B) - P(A and B)

P( FA or FC) = P(FA) + P(FC) - P( FA and FC)

0.70 = 0.55 + 0.45 - P( FA and FC)

P( FA and FC) = 0.55 + 0.45 - 0.70

= 0.30

Probability of both faulty assembly and failed components = 0.30

c)

P(FA and not FC) = P(FA) - P(FA and FC)

= 0.55 - 0.30

= 0.25

Probability of an assembly fault but no failed components = 0.25

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