John Williams of Morning Road and Cohan of Hear.

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.

That's what you want.

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.

Did she come here to relax?

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,

I'm amused by his idea of leisure.

I find his ideas about leisure interesting.

Let's say that this is our grammar

First you'll be asked if you're on business or leisure.

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

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.

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.

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).