Question
In: Math
Problem 4: A large firm uses three different types (A, B, and C) of raw materials...
Problem 4: A large firm uses three different types (A, B, and C) of
raw materials to manufacture its product. Previous records show
that 25% of the manufactured products are produced using material
A, 50% using material B, and 25% using material C. If it is known
that 5% of the product made with material A are defective, 2% made
with material B are defective, and 5% made with C are
defective.
What is the probability that a product selected at random from this
firm will be defective?
If a product selected at random from this firm is found to be
defective, what is the probability that it was made from material
A.
Solutions
Expert Solution
Let's suppose that there are total 10,000 products are produced using the three materials.
Therefore, we have:
Number of products produced by material A = 0.25 * 10000 = 2500
Number of defective products produced by material A = 0.05 * 2500 = 125
Number of products produced by material B = 0.5 * 10000 = 5000
Number of defective products produced by material B = 0.02 * 5000 = 100
Number of products produced by material C = 0.25 * 10000 = 2500
Number of defective products produced by material C = 0.05 * 2500 = 125
Therefore, we have the following tabular information:
| Non-defective | defective | Total | |
| Raw material A | 2375 | 125 | 2500 |
| Raw material B | 4900 | 100 | 5000 |
| Raw material C | 2375 | 125 | 2500 |
| Total | 9650 | 350 | 10000 |
What is the probability that a product selected at random from this firm will be defective?
Answer: 
If a product selected at random from this firm is found to be
defective, what is the probability that it was made from material
A.
milcah answered 1 year agoRelated Solutions
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