How to find probability in repeated trials?

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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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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