Please, please help-no stat experience-need answer quick-hard to stress urgency/importance

#1
Sorry, but no time to get into details. Really need to know statistical significance/calcs and probability of the following:

Theoretical Absolute Max Sample Size to randomly choose from: 21,023
2 objects selected at random from this group
2 out of 2 completely failed-no grey area, either pass or fail. Fail unacceptable.

Please explain work or refer/link to how results calculated.

Infinite thanks for your help!
 

Karabiner

TS Contributor
#2
Please explain work or refer/link to how results calculated.
Results for what? What is your precise research question (or homework question)?
Is it "how probable is it that 2 objects sampled from 21,023 fail"?
This would require to know the proportion of failures in the total
group of 21,023 objects.

With kind regards

Karabiner
 
#3
I guess the significant issue I’m trying to drive home is that, this type of device is usually only tested once because of the significant cost and time involved.

The failure of the first test was so catastrophic, so anomolous, that the agency ordered a second test be done of the exact same nature by a different company.

The second agency shockingly reproduced the exact same catastrophic failure as the first.

Again, both devices tested were selected at random from what I believe was an absolute max sample group size of 21,023 at the time. This is being extremely generous considering the testing agencies involved were most likely restricted to devices available in their local area. I may be able to figure out how many of this device were available in their particular vicinity, but I’m not sure I can get access to that data.

Being out of school for almost 20 years, I guess you could call this the most important homework problem of my life. I’m ashamed that I can’t figure this out on my own, given the fact that my grandfather played a key role in landing the first man on the moon. The initial stages of this universe’s creation/expansion/inflation (whatever we’re calling it this days) occurred in a mere heartbeat of what we understand as time. But I’ve learned first hand that it can destroy just as quickly and is indiscriminate in who it takes from us, however undeserving they may be.

I have no experience in any of the involved fields but believe there must be some scientific approach or way to mathematically express the significance of these (2) failures, especially the fact that the devices in question were selected at random and tested by (2) independent agencies, I believe each without knowledge of the other, using different equipment, literally 500 miles from one another and involved devices where failure of any kind is unacceptable: it’s basically pass or fail, 0 or 1, and failure is not an option. In these cases they weren’t just failures but I believe unprecedented in the severity of their failure.

This is just one piece of a much larger puzzle but literally (and I’m not being melodramatic) could save a life or lives.

Whether it’s probability of this occurring again or any other statistically significant value that can be calculated, anything at this point is helpful. Like I said, the cost and time involved in testing this type of device is the reason they are almost always tested only once.

Thanks again