Let's look at the measurement of this robot in its world with 5 different grid cells--
x1 through x5.
Let's assume 2 of those cells are colored
red whereas the other three are green.
As before, we assign uniform probability to each cell of 0.2,
and our robot is now allowed to sense.
What it sees is a red color.
How will this affect my belief over different places?
Obviously, the one's for x2 and x3 should go up,
and the ones for x1, x4, and x5 should go down.
So I'm going to tell you how to incorporate this measurement into our belief
with a very simple rule--a product.
Any cell where the color is correct--any of the red cells--
we multiply it with a relatively large number--say, 0.6.
That feels small, but as we will see later, it is actually a large number.
Whereas all the green cells will be
multiplied with 0.2.
If we look at the ratio of those, then it seems about 3 times as likely
to be in a red cell than it is to be in a green cell,
because 0.6 is 3 times larger than 0.2.
Now let's do the multiplication.
For each of those 5 cells, can you tell me what the result would be
multiplying in the measurement in the way I've stated.
Please, for these 5 boxes, fill out the number.