The bank is context that gives us a prior probability. However, MLE does not consider a prior. So MLE can give results that are not very helpful in the real world. All it does is answer: What parameter value (in case the probability) of a head, makes the observed outcome most likely? But it considers all parameter values equally likely. In reality, we know that it is highly likely that a random coin from a bank is a fair coin. Thus, if we flip two heads, we are almost certain that it's still a fair coin. If, on the other hand, we flipped 10 heads in a row, we might start to wonder if somehow the bank gave you a trick coin. MAP is an alternative to MLE, arguably better in many situations: [https://www.cs.cmu.edu/~aarti/Class/10701_Spring23/Lecs/Lect....