If a coin is tossed in the air, caught and flipped onto the back of the hand, most people know that there is a 50% chance of calling ‘heads’ and getting it right.
Some will also know that no matter how many times the coin is tossed, and whatever previous sequence of heads and tails has occurred, the probability of calling heads on the next toss and getting it right is still 0.5 or 50%
Alloporus contends that this is about as far as it goes.
Not many of us understand any more of the whys and wherefores of probability than the likelihood of calling head and getting it right, notwithstanding the few who take to the racing tracks. That so many others push coins into slot machines is a bit of a give away. No pun intended.
The next step on the ladder of probabilities requires intuition and so is rather hard to learn.
Suppose I have a group of 100 people.
I know that 50 of them have Irish grandparents and the other half have Scottish grandparents but there is no way of knowing the recent ancestry of an individual without asking them.
I select 10 people at random from the 100 in the room and 8 of them tell me that they have Irish heritage.
I’m expecting it to be 5 but chance can always throw things off a little. Picking just two Scots is unexpected but not impossible.
I select another 10 people at random.
Should my expectation of finding five Irish folk be the same as it was at the start?
Of course, it depends.
If I return my first 10 people to the room to resume their canapes and conversation and I select another 10 people entirely at random with no bias towards those I have already asked, then the answer is yes.
But if I send the first 10 individuals out into the carpark and sample the remaining 90 people at random then the answer is no.
Because by sending the first 10 away (sampling without replacement), I have changed the proportion of Scots in the remaining population of the room. It’s only a small amount but its no longer a 50:50 chance because the proportions of Scots to Irish is now 53:47
Hardly material to any future results. However, if I continue to sample a small population without replacement the proportional change due to my random process of sampling could affect future interpretations. Sample 30 more people and if 20 of them are Scots before we know it its a majority of kilt wearers munching on the salmon pate.
There are any number of thoughts that this simple example should generate from thinking about political poll numbers to whether or not another spin on the pokies is really worth the gamble.
Here is one that may not be at the front of mind.
It’s a truism that most of us do not get probability. My recent ‘ah ha’ moment made me realise that this ‘not getting it’ is pervasive and prevalent even among the technical folk who have been trained in it.
And people don’t get a bit of probability, it’s an all or nothing type understanding. You got the idea behind sampling with replacement not changing the likelihood of sampling a Scot or you didn’t. And it seems that if you didn’t that’s quite OK because, in all probability, you are in the vast majority.
So the thought is this.
How on earth are humans so successful when most of them do not understand chance?