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.

Now let's solve for p.

So let me put this in numbers and ask you the challenging question of what's the probability of a raise given that I'm happy and it's sunny?

Valid.

And the answer is 3.

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

How about this? Well, I'm going to apply rule one twice.

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...

We have a for statement where we'll introduce the name e as the variable name.

Oh, we were expecting a left parenthesis. Great. I just move my finger over to the right.

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.

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

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

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

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.

Here I have various combinations of open and closed parentheses.

And we have the variable P(X) with probability of 0.2, and we have 2 conditionals, P(Y_BAR_X) and P(Y_BAR_ X), both 0.6.

Here are the two rules in this grammar, P goes to open parenthesis,

And i has the value of 0.

Male narrator Here are the answers.

Let's say that this is our grammar

And the height of this 3 D surface here, that's p of x.

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

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

APPLE.

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,

Now in probability terms, people often write it as follows

Parentheses.

Next we'll use a for loop to go through the elements.

Probably not even the right concept, but that's my habit.

Just to show you how this sort of thing plays out in Python,

In fact, as a foot note, there is a measure of information called entropy.

This is 2P 3 P.

P reduces to or can be rewritten as open parenthesis P, closed parenthesis. or P can just disappear.

Let me just do this over here.

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.

Here's another way we might define find_element using index.

but it's supposed to be an I in happiness.

So chart state 0 includes the following parse states

No matter which branch you take here, you're definitely getting at least one P, but we need you to have the chance to get more.

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

This brings us to a point where we can ask one of the most fundamental questions in theoretical computer science and that is does P NP and in particular, here's what we actually know.

It takes 2 parameters to specify P of B given A and P given not A, from which we can derive P not B given A and P of not B given not A.

Well, we have two choices for our start symbol that definitely complicates things, but both of them start with a P well that's convenient since all five of our strings starts with a P.

P of C given A B is derived by a distribution over C conditioned on any combination of A and B, of which there are 4 of A and B as binary.