ABC Paper Corporation manufactures a special grade of lamina

ABC Paper Corporation manufactures a special grade of laminated (plastic coated) paper. For the current process being used, the quality control staff has shown that, on average, one defect in the lamination can be expected in every 1.25 square feet of laminated paper. A. A square foot of the product is randomly selected for inspection after the coating process. What is the chance that there is at least one defect in this area

Solution

As there is 1 defect in 1.25 sq ft, then there are 1*(1/1.25) = 0.8 defects in 1 sq ft.

As

P(at least one) = 1 - P(0)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    0.8      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.449328964

Hence,

P(at least one) = 1 - 0.449328964 = 0.550671036 [ANSWER]