Male narrator Here are the answers.

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

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.

Our agent can go north, south, west, or east, but actions may fail at random.

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.

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.

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

So that cancels out.

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

For P and P implies Q, we know that P is true in these bottom 2 cases, and P implies Q, we saw the truth table for P implies Q is true in the first, second, and fourth case.

You have to add one more argument and you have to change the returned function to implement a formula just like this but this using p0, p1, p2 as arguments not just the fixed numerical numbers here.

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

It's that grammar of balanced parentheses.

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...

Oh.

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.

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

So chart state 0 includes the following parse states

Now we can simplify these. p to the third cancels out with p to the third.

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

This one will be number 11.

This should look familiar.

I'm going to run it on a different port.

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,

Then we use append, passing in 3 as the value to append, invoking append on the variable P, and then we have an assignment that assigns the P the result of P the list 4, 5.

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

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.

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

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

Those are P51s.

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

Once we fly from X to Y, the plane is no longer at X, so we say not at P,X the plane is no longer at X and the plane is now at Y.

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

If it's false, then the flag hit will valuate to zero, 1 hit will be 1.

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

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).

So, I can rewrite this thing over here as follows

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

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

I always use P when I use url open.

Here we create a new list called q, which is an empty list. There's nothing there.

With 1 P we find ourselves right over here in the exact opposite direction.

Let's say that this is our grammar

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