A box contains 8 items in which 2 are defective.a man draws 3 items from box. Expected no. of defective items are???
Answers
no. od defective item = 8-2=6 .
probability of defective item = 3/6=1/2 .
The Expected no. of defective items are 0.703125
Given:
Number of items in box = 8
Number of defected = 2
Man draws 3 items from box at a time
To find:
Expected no. of defective items are
Solution:
Given number of defective items = 2
No of Non- defective items = 8 - 2 = 6
Let p and d be the probability of defective and non defective items
⇒ p = 2/8 = 1/4
⇒ q = 6/8 = 3/4
Number of items drawing at a time n = 3
p(x) be the event that getting defective items
As we know p(x = a) = ⁿCₐ (p)ᵃ(q)ⁿ⁻ᵃ
When no drawn items are defective
p(x = 0) = ³C₀ (p)⁰(q)³⁻⁰ = (q)³ = (3/4)³ = 27/64
When one of the drawn items is defective
p(x = 1) = ³C₁ (p)¹(q)³⁻¹ = ³C₁ (p)¹(q)²
= 3(1/4) (3/4)² = 3(1/4)(9/4) = 27/64
When both drawn items are defective
p(x = 2) = ³C₂ (p)²(q)³⁻² = 3(p)²(q)
= 3 (1/4)²(3/4) = 9/64
∴ Expected no. of defective items,
∑(X) =1xi pi= 0×27/64 + 1×27/64 + 2×9/64 = 45/64 = 0.703125
Therefore,
The Expected no. of defective items are 0.703125
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