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

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.

Let's say that this is our grammar

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.

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

APPLE.

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

Now in probability terms, people often write it as follows

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.

Male narrator Here are the answers.

It's that grammar of balanced parentheses.

Let me just do this over here.

So chart state 0 includes the following parse states

So we're going to move these dots over here and get

So that cancels out.

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

You know Walt. He would just....

The second element corresponds to my second grammar rule

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

Parentheses.

Armed with this number, the rest now becomes easy, which is we can use Bayes' rule to turn this around.

My Dad didn't like her.

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.

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

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...

Phoebe Cates is a babe.

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).

In fact, now a code every time you call the function robot and assign it say to a particle, here the i particle, these elements p i x, y, and orientation, which is the same as heading, are initialized at random.

Yeah? You never wanted that before.

He doesn't mind.

Had you absolutely decided against me, you would have acknowledged it openly.

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

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

And right here, this environment is called PyScripter.