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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 no defect - Mathematics and Statistics

Sum

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

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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!)`

P(no defects on a plywood)
= P(X = 0)

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

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

= 0.3678

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.4 | Q 1.06 | Page 152
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