
Now, the first answer is twothird, and the reason is we observed A once, and this was all we observed.

So maximum life would give us a probability of one, but because we used Laplacian smoothing,

and there's two different possible states, we add one, as before, which makes twothirds.

Twothirds is also the correct answer for the next question. There's one, two, three, four transitions out of A,

three of which leads to A again. So maximum life would give us threequarters, but because we do Laplacian smoothing,

we add one fake transition over here, and there could've been two of those, one to A and one to B, we had two over here,

which is four over six or two over three. And there's no transition out of B in this example.

So for maximum life we wouldn't even know what to say. But in our case, with Laplacian smoothing, we add one fake observation

divided by two as a denominator, so we get half for the last question.