Probability: handling uncertainty

Put likelihood on a number

Earlier we gathered data
and learned to read it by ratios and averages.
But what about things that have not happened yet?
How should we handle those?
Tomorrow has no data yet.
So we put a number on the likelihood.
Never happens is zero,
always happens is one,
and fifty-fifty sits between them at one half.
It is somewhere between zero and one.

Tap different events. The likelihood is drawn as a zero-to-one bar, also shown as a percent.

The same likelihood
is easier to grasp as a bar length.
The closer to zero, the shorter;
the closer to one, the longer.
Percent is just zero-to-one times a hundred.
One half is fifty percent, one quarter is twenty-five.
But is a coin really fifty-fifty?
Does the likelihood we set as a number
match what actually happens when we try?

Roll the die

A die has six faces.
Every face is equally likely,
so the chance of one face is one in six.
But rolling exactly six times
does not give each face once.
Three might come up three times by chance.
Here is the surprising part.
With few rolls it wobbles,
but with more rolls the share of each face
creeps closer to one in six.

Tap roll. The next face comes in a pre-set order. The more you roll, the closer each face's share gets to one sixth.

At first the bars were bumpy.
Some faces a lot, some hardly any.
But as the rolls went on,
the six bars grew more alike.
We say the share creeps
closer to the true probability.
So from one or two results
you must not jump to conclusions.
Only with many does the true shape show.
Then what about the chance of two things
happening together at once?

Two things happen together

A coin lands heads, and at the same time
a die shows six, what is the chance of both?
The two are unrelated.
In that case we multiply each one's chance.
Heads is one half, a six is one in six.
Multiplied, it grows smaller.
Think about it and it makes sense.
Both must be likely
for the pair to be likely.
The more conditions, the harder both happen together.

Pick and combine two events. Watch their chances multiply, so the chance of both grows smaller.

Multiplying the two chances
made the result smaller than either one.
Things happening together are that much rarer.
This fits our gut feeling too.
It is hard for several lucky breaks at once.
Now let's see what probability is good for.
When the world is not certain,
we can compare the chances
and pick the most likely side.

Pick the most likely side

Even when we cannot know for sure
a decision still has to be made.
Then we score each candidate's chance
and pick the biggest one.
If the animal in a blurry photo
is a cat with chance zero point seven, a dog zero point two,
we answer cat.
It could be wrong,
but it is the most likely answer.
This is exactly how AI picks an answer.

Tap the blurry clue. Each candidate gets a probability, and the most likely answer is chosen. It is decided by likelihood, not certainty.

AI does not declare it knows the answer.
It scores several candidates with probabilities
and offers the biggest one as its answer.
So for the same picture,
if the chances are close it seems unsure,
and if one is large it answers with confidence.
This picking by likelihood
is the seed of the big model we will learn next.
Even choosing a single letter,
it picks the most likely next letter by probability.

Let's wrap up

Gathered on one line, it is this.
Probability puts likelihood on a number between zero and one.
Try many times, like a die,
and the share creeps closer to the true probability.
The chance of two things together
is each one's chance multiplied.
And when it is not certain,
we pick the most likely side.
AI picks its answer by probability just the same.

Tap the key points in order to review. (likelihood as zero to one -> many tries converge the share -> together is a product -> pick the most likely side)

Now you know how to handle
things that are not certain, as numbers.
The daunting fog of chance
became graspable as a number between zero and one.
With many tries the share settles,
and even without certainty we can pick
the most likely side, which is real power.
Next, with this picking by probability,
let's go on to the story of big models
that make text and pictures.