Let's suppose there are $2$ heavily biased coins such that coin A has a bias of coming up $90$% heads and coin B has a bias of coming up $90$% tails. Both coins are placed in a bag and one is randomly chosen in a way that either coin is equally likely to be chosen and cannot be identified as either A or B. The coin is tossed fairly $10$ times and it is observed that $10$ heads came up.
Then if someone were to ask that if that same coin is tossed $10$ more times, what is the number of heads expected, can we assume at the point that it is coin A or can we not assume that and just say we would expect $5$ heads on average? That is, since the $10$ "given" heads is not a $100$% definitive indication of what coin we have, must we say that it could be either coin A or coin B or can we "bias" our answer towards coin A and say that we expect something like $9$ out of $10$ heads instead of just $5$? However, if we do that and we "guess" wrongly, (that is it was actually coin B), then our estimate will likely be WAY off! Should we assume that it is more likely that coin A was chosen than coin B and thus our answer will be affected? If so, then how do we compute the number of expected heads?
The "problem" is that in the shortrun, even a heavy bias may not "pan out" to the expected outcome. For example, maybe this experiment was tried millions of times and this short (relative to millions) observed outcome just happened to be $10$ heads in a row but it was actually coin B that did this.