Pattern Recognition and Machine Learning : 1-2 Probability Theory

A key concept in the field of pattern recognition is that of uncertainty.
We will introduce the basic concepts of probability theory by considering a simple example.
Imagine we have two boxes, one red and one blue, and in the red box
we have 2 apples and 6 oranges, and in the blue box we have 3 apples and 1 orange.
This is illustrated in Figure .
Now suppose we randomly pick one of the boxes and from that box we randomly select an item of fruit, and having observed which sort of fruit it is we replace it in the box from which it came.
We could imagine repeating this process many times. Let us suppose that in so doing we pick the red box 40% of the time and we pick the blue box 60% of the time, and that when we remove an item of fruit from a box we are equally likely to select any of the pieces of fruit in the box.

Example 1.2 Polynomial Curve Fitting