And then here's my favorite quote from one of the girls

So this is going to be minus 2p right over here.

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 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.

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

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.

So this right here becomes, you have this p right over here, so this is equal to p.

So that cancels out.

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

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

Wedlock is a padlock.

Let's say that this is our grammar

P of X3 given X1 is the sum of P of X3 given X1 and A times P of A given X1 plus the A complement, which is X3, conditional X1 and not A times P of not A given X1.

In these other examples we were picking 30 percent, but now we can say it's p, it's the percentage off.

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

We obtained P of A0 given X0 through base rule, which should look very familiar at this point.

Let me just do this over here.

It's that grammar of balanced parentheses.

So chart state 0 includes the following parse states

Now let's add that pink p to both sides of this equation.

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

Let me do the mean in white.

The first one looks pretty good. I just apply rule 1.

Those are P51s.

P of happiness given S and R times P of S and R, which is of course the product of those 2 because they are independent, plus P of happiness given not S R, probability of not as R plus P of H given S and not R times the probability of P of S and not R plus the last case,

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

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.

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

So let's say that that's the nucleus and I'll just draw their p orbitals.

So, I can rewrite this thing over here as follows

P

p.

What's next?

P .

P ... P ...?

Teacup!

Similarly, over here I'm going to apply rule one three times.

P...

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 expression is called the likelihood.

The second element corresponds to my second grammar rule

So, of the 8 possible outcomes of the coin flips, those 3 are the ones you want to count.

Valid.