Mathematical probabilities (Sampling Inspection)

P

Palt88

#1
Hi There,

Sorry for this silly question, but I'm unable to remind my old mathematics rules...

I would like to know for a population of let's say 10000 parts that includes 5 defect parts.

If a sample of 125 is taken, what is the probability to get the 5 defect parts in the sampling?

I guess it start like that: 5/10000 x 4/9999 X 3/9998 X 2/9997 X 1/9996...
but I can't remember how to compute the 125 samples around?

Thanks
 
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Tim Folkerts

Super Moderator
#3
I guess it start like that: 5/10000 x 4/9999 X 3/9998 X 2/9997 X 1/9996...
but I can't remember how to compute the 125 samples around?
That would give you the probability of drawing the five defects as the first 5 items you drew and then drawing 120 good items. It works out to about 1.2E-18

Then you need to multiply by how many ways you can arrange the 5 defects among 125 items dawn. That would be 125! / 120!*5! = 234531275

So hte overall odds of getting all 5 seem to be

234531275 / 1.2E-18 = 2.8E-10


As a simple approximation, your sample of 125 out of 10000 parts is 1/80 of the parts. The odds of finding each defect in that 1/80 of the parts is 1/80. The odds of all of them being in that 1/80 is 1/80^5 = 3.05E-10. Since that is about the same as the previous answer, then I am pretty sure there is no mistake in the original calculation.
 
P

Palt88

#5
Good results guy...

I went in excel with the following formula:

=HYPGEOMDIST(5;125;5;10000)

and gives 2.81719E-10

:agree:

P.S: Tim, in you calculation 234531275 / 1.2E-18 = 2.8E-10
, it is not a / but a *
 
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