1. The problem statement, all variables and given/known data A manufacturing machine produces defects with a probability of 0.1%. How many parts must the machine produce to have a 99.9% chance of producing at least 1 defective part? 2. Relevant equations P(A) + P(B) = 1 3. The attempt at a solution A in this case is the machine produces at least one defective part B is the case when the machine produces all good parts The probability that the machine produces a good part in the first try is: P(B) = 1 - .001 = .999 The probability that the machine produces two good parts consecutively is: P(B) = .999*.999 = .999^2 So I assume the probability that the machine produces n good parts consecutively would be: P(B) = .999^n Therefore the probability that the machine produces at least 1 bad part part within n consecutive parts must be: P(A) = 1 - .999^n Using P(A) = .999 and solving for n. .999 = 1 - .999^n ln(.001)/(ln(.999) = n = 6904.3 = 6905 parts Does that make sense? That we need to produce 6905 parts to have a 99.9 percent chance of 1 defective part?