I computed the probabilities by approximating it by taking a large set of points. Here is what I did:

After the run of PLA we have the g function ( in the form of weights )

We also have the f ( since we generated it )

Now create a large number ( L ) of fresh random points in the space

Check how many of these points have f(x) != g(x); call it 'Error'

Compute the probability = Error/L

Note:

I don't know if this method is correct or not.

I don't know what is the value of L that is "sufficiently large";

I used L = 1000000

The computed probabilities will very ( You may want to take an average )

I got the answers correct

( May be by luck )

If any of you tried the approximate computing method, can you please share your ideas.

Thanks,

Bipin