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प्रश्न
There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?
उत्तर
Let X denote the number of defective items.
P(getting defective item) = p =
∴ q = 1 – p = 1 – 0.1 = 0.9
Given, n = 4
∴ X ∼ B(4, 0.1)
The p.m.f. of X is given by
P(X = x) =
P(sample will include not more than one defective item)
= P(X ≤ 1) = P(X = 0 or X = 1)
= P(X = 0) + P(X = 1)
=
= (0.9)4 + 4 x 0.1 x (0.9)3
= (0.9)3 (0.9 + 0.4)
= 1.3 x (0.9)3.
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