How to find probability in repeated trials?

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Homework Help Overview

The discussion revolves around a probability problem related to reliability engineering, specifically focusing on determining the number of trials needed to achieve a certain probability of finding at least one defective product given a known defect rate.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the binomial probability formula to find the number of trials needed for a specified probability of detecting at least one defect. Some participants question whether the approach of setting k=1 is appropriate for the requirement of finding at least one defective product.

Discussion Status

Participants are actively engaging with the problem, offering clarifications regarding the interpretation of the probability formula. There is a recognition of the need to consider the probability of no failures, which may provide a more straightforward path to the solution.

Contextual Notes

The original poster expresses uncertainty about their foundational knowledge in probability and statistics, indicating a potential gap in understanding that may affect their approach to the problem.

TiredEngineer
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Info: I made the mistake of starting engineering grad school years after finishing my undergrad, and forgot my basic prob/stat. This is related to reliability engineering.

Homework Statement



How many arbitrarily selected units do I have to test so that my probability is 0.85 of finding one at least one defective product if I have a 0.05 defect rate for this particular product.

Homework Equations



Binomial Probability Formula

binomial%20probability%20formula.gif


The Attempt at a Solution



I tried setting the formula to be equal to 0.85, k=1 (because I only need one to fail), and left number of trials as "n" to solve for. I have tried to solve for this and was having a tough time, and I am not even sure if this is the correct approach.

Edit: p=0.05 and q=1-p=0.95
 
Last edited:
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TiredEngineer said:
Info: I made the mistake of starting engineering grad school years after finishing my undergrad, and forgot my basic prob/stat. This is related to reliability engineering.

Homework Statement



How many arbitrarily selected units do I have to test so that my probability is 0.85 of finding one at least one defective product if I have a 0.05 defect rate for this particular product.

Homework Equations



Binomial Probability Formula

binomial%20probability%20formula.gif


The Attempt at a Solution



I tried setting the formula to be equal to 0.85, k=1 (because I only need one to fail), and left number of trials as "n" to solve for. I have tried to solve for this and was having a tough time, and I am not even sure if this is the correct approach.

Edit: p=0.05 and q=1-p=0.95

The probability of getting at least one failure after k trials is one minus the probability of getting no failures after k trials. You should find the 'no failures' case easier to solve.
 
What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.
 
What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.
 
Thanks for the help guys. That was a herp-derp moment for me.
 

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