0.385 is the probability under given conditions.
Lets simplify the above problem,
Given n=20, p=0.05, q=0.95
Probability that in a sample of 20 window frames:
None will need adjustments.
P(x=0)= 0.95^20 = 0.3585
At least one will need adjustment?
P(x>=1) = 1 - P(x=0)
= 1 - 0.3585
= 0.6415
More than two will need adjustment?
P(x>2) = 1 - P(x=0) -P(x=1) -P(x=2)
= 1 - 0.3585 - 20C1(0.05)^1*(0.95)^19 - 20C2(0.05)^2*(0.95)^18
= 0.6415 - 20*0.05*0.3774 - 190*0.0025*0.3972
= 0.2641-0.18868
= 0.0755
Hence 0.385 is the solution of the given problem.
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