So you can figure out the answer by intuitive reasoning, or you can figure it out by going to the conditional probability tables and seeing according to the definition of conditional probability whether the numbers work out.

For secret, we know it to be 1 3.

In this case, there's only one such variable, Cloudy.

In this case, R and T.

And this is the P value that you see reported in, in research.

When we apply the same rule as before, we get the prior for spam which is 3 8.

But if you understood Laplacian smoothing, you might want to give it a try.

In the next video I'll do a lot more examples with the free throws and the basket, and we'll even learn a little bit about conditional probability.

We would say that we reject the sample, and this technique is called rejection sampling.

Now we'll draw out that table.

That is more complicated than everything else we've talked about so far.

Conditional Styles

Conditional Styles...

There is a condition attached.

Check out this Bayes network over here, which is defined by the following conditional probability table

The probability of a negative test and having cancer, and this is not conditional anymore.

The first operation in variable elimination is called joining factors.

We know the prior probability for A, and we know the conditional.

And then, let's just divide both sides by a.

There is an initial state distribution for the time step 0.

What's the probability that this coin comes up heads?

That gives us a new network with T and L with these conditional probability tables.

least maybe it doesn't make intuitive sense just yet, but I showed you that the probability of a and b is equal to the probability of a given b times the probability of b.

Now that variable is defined, we can choose another variable.

So if the first outcome was heads, you pick a coin whose probability of coming up heads is going to be 0.9.

And we get this, the probability of b given a is equal to this, probability of a given b.

Accept cond.

The same thing.

Remove Conditional Styles

Now the next step is to say we can factor this and take these individual variables write that in terms of conditional probabilities.

Please remember what that P value really means.

And C can be, C1, C2, C3.

Accept invitation conditionally

And technically speaking, that P value is a conditional probability.

About conditional inclusion

Remove Conditional Formatting

Add Conditional Formatting

Remove the conditional cell styles

Let's ignore that.

But you can see this is a generalisable thing.

There's a probability I got a two sided coin.

And then given that, what's the probability that

Let me just say it a little bit abstract.

So there're important lessons in what we just learned, the key thing is we talked about conditional probabilities.

But we don't know for sure that they're exclusive events.