Another way to think about that is let's say that we're in a particular state like this one

And if you want to factor a p out of this, this is going to be equal to p times, if you take p divided p you get a 1, p square divided by p is p.

P of A given B where B is the evidence and A is the variable we care about is P of B given A times P of A over P of B.

The first line's P. Sherman.

So p times 1 minus p, which is a pretty neat, clean formula.

And the sentences are P or not P, P and not P,

And then this term over here, this whole thing over here, is going to be plus p times 1 is p. p times negative 2p is negative 2p squared.

So, to get all 3 of them together, we just multiply these by 3.

Let's say that this is our grammar

The second thing we learned has to do with negation of probabilities.

P. Sherman, 42 Wallaby Way, Sydney.

Once again, based on this P, I'm going to start bringing in rules 1 and 2.

You can actually compute this using total probability where P(Y) equals P(Y_BAR_X) times P(X) plus P(Y_BAR_ X) times (P X).

F, L, E, P, T, P L, E, P, F, L, F, L, E, P, T, P, L, F, E, T.

APPLE.

Now in probability terms, people often write it as follows

Why English? In a single word opportunity.

It takes 1 parameter to specify P of A from which we can derive P of not A.

Just be careful. I love you.

Nothing better than that.

Thanks.

Let me just do this over here.

Starting from s, I can take rule let's do 0.

This is going to be, this term right over here is going to be p squared minus p to the third.

So chart state 0 includes the following parse states

But what if you want to include quoted dialogue in your string?

All right. E, F, L, E, P, T P, L, E, P, F, L, E L, E, P, T, L, P, E, F, E, T, Z, E, T...

This one will be number 11.

P. Sherman, 42 Wallaby Way, Sydney.

I'd better say hello.

And then when you add p squared to negative 2p squared you're left with negative p squared minus p squared.

Rule 0 and rule 1 both apply to S, so I'm going to yield 2 things.

A better day that will never come

So that cancels out.

So this is going to be equal to 1 minus p.

If you square it you're just going to get p squared.

And then plus negative p squared.

So we said that this is equal to e to the r, so p times this is equal to p.

Now, you might be tempted to say What about the probability of X given not Y?

So what I want you to do is tell me for each of these sentences, whether it is valid, satisfiable but not valid, or unsatisfiable, in other words, false for all models.

In the 19th century,

You are somebody who is so passionate.

Better call the cops.

A better day yet to be made

Thank you for remembering.