Disclaimer: Sorry, i'm a self-taught non-native, apart from basics, i don't know the proper terms. I'm pretty sure there has to be a part of statistics that would help me deal with my problem, but somehow i'm unable to word my question well enough for google to be helpful.
What if i'm observing fake coin being tossed. Say the coin's heads-chance is some random number (could be anything from 0% to 100%, all numbers equal...i hope uniform distribution is the correct term). Now i saw the coin being flipped X times (could be 10, 100 or millions) and get heads Y times. Now obviously i could say "This is most probably Y/X head-chance coin", but what if i wanted something like a histogram? Something that would let me say "I'm 90% sure that coins head-chance is between 60% and 80%, 4% sure it's between 80% and 90%, 4% sure it's between 50% and 60% and so on..."
I'd appreciate even non-complete answers or pointers, "Go study X-E-omega-effect" or such would be helpful as well.
What you are thinking of is Bayesian statistics. Call the chance of heads $p.$ Then what you are basically saying is
This is exactly the idea of Bayesian statistics. The distribution of $p$ before you observe the data is the prior (in this case a uniform distribution). The distribution of $p$ after you've observed the $X$ coin flips is called the posterior distribution (which you need to work out mathematically).
I could point you towards some more sources, but it's hard to do so without a better idea of your current level. The terms Bayesian statistics and Bayesian estimation should help you help yourself though.