Question

A sample of 4 items is selected
of random from a box containing
12 items of which 5 are defective
Find the expected no. E of the
defective​

Answer 1

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 defective​s

= 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 defective​s  is 1.667

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