The crop of undergraduate biology students of which I was a member was doing badly at statistics. We would not be allowed to pass biology without performing at least adequately in this essential step of analysing experimental data, without which research results can fall into mere wish fulfilment and speculation. So the biology department made an arrangement with the mathematics department to take us on for group coaching by a couple of young PhDs. They would show us in a hands-on manner how real life events demonstrate the mathematics of probability and its practical metric, statistics.
One of our classes involved getting into small groups and doing coin tossing, measuring the frequency of heads and tails and plotting the statistical graphs to show the normal pattern produced. During this process the tutors went from group to group, observing our progress. But something went sideways in my group. We could only throw heads. Head… head… head… head… head… It started getting silly and we started laughing and getting excited, which attracted attention. The tutors came to watch. Head… head… head… head… head… The rest of the class came to watch. Head… head… head… head… head… Before long everyone was craned over our table watching this endless progression of heads, waiting for a tail to come and break the sequence, in the direction of restoring normality.
But it never did. The coin was sent down to the physics department for testing. Was its weight distribution uneven? Did it have some distortion that affected its aerodynamic properties? Did it vary outside the normal range for its type of coin in any way? The answer came back: no. It was a normal, true, balanced coin no different from all the others.
So the tutors calculated the probability of this event which had just occurred: one in billions. Trust a bunch of life scientists to blow away the comfortable little premises of statistics! Contemplating this event over the years, it tells me that we are unwise to limit Reality to our narrow little concepts of how things are supposed to be and what is considered normal, usual, probable or possible.