a sample of 4items is selected at random from a box containing 12 items of which 5are defective. find the expected no.of defective items
Answers
Step-by-step explanation:
selected from among 12 = 12/(81)(4!) = 495. Those possible with 0 defective items = [5!/(5) (017/(31)(41) = 35. Those possible with 1 defective item = [5!/(41) (11[7V(49(31) = 175. Those possible with 2 defective items = [5/(31) (2)][7/(51)(21) = 210. Those possible with 3 defective items = [5/(2) (3)|[7/(61)(11) = 70. Those possible with 4 defective items = [5!/(11) (41)|[7U(79(01) = 5. Thus, there are 460 possible combinations of 4 items, selected as described, which include at least 1 and up to 4 defective items. Just 35 possible combinations of 4 items include none that are defective.
Given: A sample of 4 items is selected of random from a box containing
12 items of which 5 are defective
To Find: the expected no. E of the defectives
Solution:
Total = 12
Defectives = 5 , Non defectives = 7
0 defectives = ⁷C₄.⁵C₀/¹²C₄ = 35/495
1 defectives = ⁷C₃.⁵C₁/¹²C₄ = 175/495
2 defectives = ⁷C₂.⁵C₂/¹²C₄ = 210/495
3 defectives = ⁷C₁.⁵C₃/¹²C₄ = 70/495
4 defectives = ⁷C₀.⁵C₄/¹²C₄ = 5/495
expected no. E of the defectives
= 0 * 35/495 + 1 * 175/495 + 2 * 210/495 + 3 * 70/495 + 4 * 5/495
= ( 175 + 420 + 210 + 20)/495
= 825/495
= 1.667
expected no. E of the defectives is 1.667
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