oo Ooredoo 4G 12:10 PM a mybb.qu.edu.qa only one defective device? 5-What is the

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oo Ooredoo 4G 12:10 PM a mybb.qu.edu.qa only one defective device? 5-What is the probability to select a sample that has no defective device? Exercise#4 A given firm is producing some electronic devices. Before packaging and delivery stages, some quality control tests are often conducted to ensure the reliability of the products. The firm data shows that 85% of the items are conform (C) and 15% are defective (D). Among the defective devices only 20% can be repaired (R), the rest are scrapped (waste) (S). Assume items failures are independent. Use the above introduced abbreviation C, D, R and S for all the answers (probability statements). 1-Knowing that is defective, what is the probability that a device will be scrapped? 2-What is the probability that a randomly selected device 3-An item is selected randomly, what is the probability that this item will NOT be scrapped? 4-What is the probability to select an item that must be scrapped after analyzing exactly 5 devices? 5- What is the average number of items that should be analyzed to select an item that will be scrapped?

Explanation / Answer

P(C) = 0.85

P(D) = 0.15

P(R | D) = 0.2

1) P(S | D) = 1 - P(R | D) = 1 - 0.2 = 0.8

2) P(D and R) = P(R | D) * P(D) = 0.2 * 0.15 = 0.03

3) P(S) = P(S | D) * P(D) = 0.8 * 0.15 = 0.12

P(S') = 1 - P(S) = 1 - 0.12 = 0.88

4) Probability = 0.884 * 0.12 = 0.072

5) expected value = 1/0.12 = 8.33

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