How to find probability in repeated trials?

[TiredEngineer]

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

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

 

[Dick]

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

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.

 

[haruspex]

What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.

 

[haruspex]

What Dick said. To elaborate, setting k=1 gives the probability of exactly one failure - you want at least one.

 

[TiredEngineer]

Thanks for the help guys. That was a herp-derp moment for me.