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thepatient
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Homework Statement
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?
Homework Equations
P(A) + P(B) = 1
The Attempt at a Solution
[/B]
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?
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