Question

The defects on a plywood sheet occur at random with an average of the defect per 50 sq. ft. What Is the probability that such sheet will have-

(a) No defects
(b) At least one defect 
[Use e^-1 = 0.3678]

Answer 1

Let random variable X = number of defects. Here X follows Poisson distribution.
Given mean = λ = 1

X ∼ P(1) 

p.m .f ia P(X = x) = `(e^-1 xx 1^x)/(x !)`

(a) P(no defect) = P(X = 0) 
                         = `(e^-1 xx 1^0)/(0 !)`
                         = `(e^-1 xx 1)/(1)`
                         = e^-1 = 0.3678

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