A roll of cloth has localized defects randomly distributed O

A roll of cloth has localized defects randomly distributed. On average there is one defect per square yard. Find the probability that a piece of three square yards has more than two defects, given that it is not defect free.

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

On average there is one defect per square yard, as per it for 3 yards the mean rate could be 3

P( X < 2) = P(X=1) + P(X=0)   
= e^-3 * 2 ^ 1 / 1! + e^-3 * ^ 0 / 0!
= 0.1991
P( X > = 2 ) = 1 - P (X < 2) = 0.8009