# 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 at least one defect. Use e−1 = 0.3678. - 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 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!)

P (at least one defect)
= P (X ≥ 1)
= 1 – P (X = 0)
= 1 – 0.3678
= 0.6322

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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