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Question
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:
- no defect
- at least one defect
Use e−1 = 0.3678
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
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