Find the probability a seam needs reworking
I'm redoing some homework for practice and I came across a problem I can't think of a way to solve.
An aircraft seam requires 25 rivets. The seam will have to be reworked if any of the rivets is defective. Suppose rivets are defective independently of one another, each with the same probability.
A. If 15% of all seams need reworking, what is the probability that a rivet is defective?
B. How small should the probabaility of adefective rivet be to ensure that only 10% of all seams need reworking?
How do I solve this? Could you point me in the right direction? I have a few formulas but I don't see any links here.
The answers are .00648 and .00421 respectively.
$\endgroup$1 Answer
$\begingroup$If $p$ denotes the probability that a rivet is defective then $(1-p)^{25}$ is the probability that none of the rivets are defective, and $$1-(1-p)^{25}$$ is the probability that there is at least one defective rivet. So, we have the following equation for $p$: $$1-(1-p)^{25}=0.15.$$ That is $0.85=(1-p)^{25}$ from where $p$ can be determined.
Now, if we want that the seam be defective only with probability $0.1$ then we have to solve another equation:$$1-(1-p)^{25}=0.1.$$
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