We'll start with an example.
Let's say we're in an office and there are two people,
Alex and Brenda, and they're both there the same amount of time.
When they were in the office and we see someone passing by really fast,
we can't tell who it is,
but we'd like to take a guess.
So far, with all we know,
all we can infer is that since they're both in the office the same amount of time,
the probability of the person being Alex is
50 percent and the probability of the person being Brenda is also 50 percent.
But now, let's try to use more information so we
can make a better guess of who the person is.
When we saw the person running by,
we notice that they were wearing a red sweater.
So, we'll use that piece of information.
We've known Alex and Brenda for a while,
and actually we've noticed that Alex wears a red sweater two days a week,
and Brenda wears a red sweater three days a week.
We don't know which days, but we are sure of this fact.
Also, when we say week we mean workweek,
so five days, although at the end this won't matter much.
So now what we'll do,
is we'll use this piece of information to help us make a better guess.
First off, since Alex wears a red sweater less than Brenda,
It's easy to imagine that it's a bit less likely that
the person we saw is Alex than that it is Brenda.
But exactly how likely?
Well, let's say that if we saw a person pass by five times,
it would make sense to think that two of this times it was Alex,
since he wears a red sweater twice a week.
And the other three times it was Brenda,
since she wears a red sweater three times a week.
Therefore, from here we can infer that the probabilities are 40 and 60.
We've used the formation about the color of the sweater to obtain
better probabilities about who was the person who passed by.
This is Bayes' theorem and we'll learn in more in detail in the next few videos.
The initial guess we had, the 50/50 guess,
is called the prior,
since it's all we could infer prior to the new information about the red sweater.
The final guess we have,
the 60/40 guess is called the posterior,
since we've inferred it after the new information has arrived.