So obviously, in this binomial distribution, there are about 16 different outcomes from 0 to 15.

And of course, it's near this one.

let me ask you a couple of easier questions what is the most likely outcome for 11 coin flips assuming that the H₀ is correct and the answer is 3.

The odds are against you, colonel.

Sham has about as much chance of beating Secretariat as Pancho has of beating Muhammad Ali.

Check the box that is the most likely µ you might observed, if p is a true probability using our statistical estimator.

Here are the outcomes and here are the probabilities.

And that makes it extraordinarily interesting as a place to explore.

I would say, HlV is very different in Africa.

So for comparison's purposes, let's think about some other walk of life you may expect might be extremely risky.

Actually, just let me write first green

So what is the probability of winning if you always switch?

Well, let's improve the odds.

He's got a good track record.

Because the risk, the high probability of climate change is real.

That's what we're seeing across the bottom billion at the moment.

So if you get a positive test result you're going to raise the probability of having cancer relative to the prior probability.

I expect my second test to be positive with probably 0.2301.

That sounded tight.

How awesome would that be?

You can drive it, but there's still the occasional accident.

the risk is too high.

Now this format begins to look very much like the game tree that we talked about in the previous unit.

So the probability of the first marble being green and the second marble being green

The smallness of that probability is what we mean by extremity.

And now we have 70 percent since 20 years, it's the highest rate of separation of garbage in the world.

It's kind of the big thing in application and machine learning.

You're in the gang for four years, you expect to die with about a 25 percent likelihood.

After now closing the curtain again, he'll ask you do you want to switch.

Well, it's going to be the probability that you initially picked wrong.

Here's a game tree for a stochastic 2 player game.

Good? Yeah, No, I'm great, you know, it's totally great.

looks the data has a very high probability of being in the central region, low probability of being further out, low probability of being further out, and so on.

If it comes up tails, you get nothing.

Then the value of the state for the action go up would be obtained as follows.

That is, out of all the possible values for all the query variables, which combination of values has the highest probability?

Probability

Phil, the odds against

We know that at time 0 it was raining with half a chance.

Hector commands the finest army in the east.

What happenned in the past in these flips does not affect the probabilities going forward.

For example, in the last row we have a r and a t. r is 0.9.

You might have heard about Bayes Rule before.

Very good.

The way that more of you are likely to die than the combination of all three of the others that you see on the slide.