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 8 months ago

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