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Defects on plywood sheet occur at random with the average of one defect per 50 sq. ft. Find the probability that such a sheet has (i) no defect, (ii) at least one defect. Use e−1 = 0.3678. - Mathematics and Statistics

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Defects on plywood sheet occur at random with the average of one defect per 50 sq. ft. Find the probability that such a sheet has (i) no defect, (ii) at least one defect. Use e−1 = 0.3678.

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Solution

Let X denote the number of defects on a plywood sheet.
Given, m = 1, e–1 = 0.3678

∴ X ~ P(m) ≡ X ~ P(1)

The p.m.f. of X is given by

P(X = x) = `("e"^-"m" "m"^x)/(x!)`

∴ P(X = x) = `("e"^-1 (1)^x)/(x!)`

(i) P(no defects on a plywood)

= P(X = 0)

= `("e"^-1 (1)^0)/(0!)`

= `(0.3678 xx 1)/(1)`

= 0.3678

(ii) P(at least one defect)

= P(X ≥ 1)

= 1 – P(X = 0)

= 1 – 0.3678

= 0.6322

Concept: Random Variables and Its Probability Distributions
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