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प्रश्न
The defects on a plywood sheet occur at random with an average of the defect per 50 sq. ft. What Is the probability that such sheet will have-
(a) No defects
(b) At least one defect
[Use e-1 = 0.3678]
उत्तर
Let random variable X = number of defects. Here X follows Poisson distribution.
Given mean = λ = 1
X ∼ P(1)
p.m .f ia P(X = x) = `(e^-1 xx 1^x)/(x !)`
(a) P(no defect) = P(X = 0)
= `(e^-1 xx 1^0)/(0 !)`
= `(e^-1 xx 1)/(1)`
= e-1 = 0.3678
(b) P (at least one defect) = P(X ≥ 1)
= 1 - P(X = 0)
= 1 - 0.3678
= 0.6322
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