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 :(a) no defect(b) at least one defect(use \(e^{-1}=0.3678\))

Q.6 (A) (iii) 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 :
(a) no defect
(b) at least one defect
(use \(e^{-1}=0.3678\))

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: (a) 0.3678 (b) 0.6322

Let X = number of defects on a sheet (of 50 sq. ft). X follows the Poisson distribution with \(m=1\): \(P(X=x)=\frac{e^{-1}1^x}{x!}\).

(a) \(P(X=0)=e^{-1}=0.3678\)

(b) \(P(X\ge1)=1-P(X=0)=1-0.3678=0.6322\)

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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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 :(a) no defect(b) at least one defect(use \(e^{-1}=0.3678\))

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