Suppose there's a weighted coin. That coin either lands on heads every 1/10 times it is tossed, or it never lands on heads at all. I don't know whether that coin is the type of coin that lands on heads 1/10 of the time, or if it's the type of coin that never lands on heads, but I want to figure this out by tossing the coin many times.
Suppose I toss the coin 20 times and it's Tails every time. What's the probability the coin is the type of coin that never lands on heads? Generally, how would I figure this kind of thing out for some other number of times, or some other "coin flip" probability?
Edit: this isn't a homework problem. I'm just used to thinking in "homework problem" language since I don't normally do this kind of math day to day.
I'm a software engineer trying to get rid of an intermittent issue that happens somewhere around 1/10 of the time. I want to be able to say I fixed it with, say, 95% confidence after running a test some number of times. It's an expensive test to run, so I don't want to run it more than I have to to be nearly certain it's fixed.