Mathematical Conundrum or Not? Number Six Consider this: Say I have an unfair coin, on average it flips H 9 out of 10 times. You don't know this; however, all you see is a coin and without knowing it is unfair you give H a 50% chance. That is the difference between subjective and objective probability.
The only way for you to know that the coin flips H 9 out of 10 times is to flip the coin several times. Maybe I flip it for you a few times, say I get four heads in a row, and you are starting to doubt your 50/50 assumption. Then I flip it more and get two more heads, now you no longer believe it is 50/50.
That's Bayesian inference in a nutshell.