Answer to Question #131909 in Statistics and Probability for Hadia

Question

Defects in large plates of glass occur ,on average ,one per 10 square feet .what is probability that a 6x10 sheet will contain no defect.

ii. At least one defect?

Answer 1

Average is one per 10 square feet , This is a poison with each portion of one unit = 10 square feet,

Now in 6x10 there is 60 square feet,thus these are 60/10 units = 6 units

(i) probability of no defect = P(x; μ) = (e^-μ) (μ^x) / x! where μ= 1,x=0

p(0) = (e^-1) (1⁰) / 0! = 0.3679, thus the probability of no defect is 0.3679

(ii) p(x>0)= total probability -probability of zero defects

p(x>0) = 1-0.3679 =0.6321

Thus the probability of at least one defect is 0.6321