Let's say, the Probability of getting a tails on the first flip, getting a heads on the second flip,

Now let's see a slightly complicated example

So suppose we toss a coin repeatedly.

And getting a tails on the third flip. So this is going to be equal to the probability of getting a tails on the first and third flip, and a heads on the second

You know, some people feel that if they got 5 heads in a row that they're more likely to get a tails on the sixth time.

So, because these are independent events we can say it is the same thing as the probability of getting tails on the first flip, times the probability of getting heads on the second flip, times the probability of getting tails on the third flip.

I think it backfired.

That could be as you can tell, I switched colors arbitrarily.

laughter

Remember, in this case, the position of heads or tails, first, second or third does not affect

Their probability

Another way of thinking about it if we tossed a coin eight million times, then we'd expect a million head tail heads and a million head tail tails but the head tail heads could occur in clumps.

Once again these are all independent events the fact that I got tails on the first flip in no way affects the probability of getting a heads on the second flip and that in no way affects the probability of getting a tails on the third flip.

And the answer is 2.

Flip one can come of heads or tail same for flip two, heads, tail, heads, tail and the same for flip three and if you look at this every possible combination is represented.

I'm saying this exact order the first flip is a tails, second flip is a heads and then third flip is a tail.

We would say maybe a little bit more frequently but let's flip it more often.

Let me just draw them, and say it's a fair die, which means each of the different sides comes up with a probability over 6 for any of the numbers you can plug in over here.

If you, once again, draw the truth table, you find, for the different combinations, that if you've drawn coin 1, you'd never see tails.

And for some reason which shall remain rather vague we're interested in a particular pattern.

And the answer is 1.

In fact, sometimes she gets so friendly that it backfires and men get the wrong idea.

For instance, there's eBird, where amateur birdwatchers can upload information about their bird sightings.

In this case I pick a coin which with 0.8 probability will once again give me tails, conditioned on the first coin flip coming up tails.

page is the input that's something that changes and we want to make the URL that's the result we want an output.

Right?

And the reason why, you know, I could make a symmetry argument that it's just as likely to go on heads as it is to tails.

I could get a head on the first flip and a head on the second flip, head on the first flip, tail on the second flip,

We've taken initial pick of the coin, which can take coin 1 or coin 2 with equal probability, and then you go flip it for the first time, and there's heads or tails outcomes, and we flip it for the second time with the second outcome.

So, for flip 1, we have the outcomes of heads, heads, tails, tails.

They got this way by being remarkable, sometimes a little too remarkable.

And I can check to see if an element is in a list in Python just by using the keyword in putting the element on the left and the list on the right.

I don't know which one I have picked. It might be fair or loaded.

The way I word this is by conditional probability, probability of the second coin flip coming up heads provided that or given that X1, the first coin flip, was heads, is 0.9.

It's asking for some type of way of getting your hands around an event that's fundamentally random.

Before we put the money into the briefcase, we'll sew it into the lining.

So you might think there are more interesting things to do, but humor me for the moment.

Now, I'm going to make it really difficult. I'm going to give you a coin let's call it loaded.

Did you know all chemical matter follows certain laws as well?

First of all, it was a pirate supply store, which is insane.

A T distribution with 9 degrees of freedom.

Complete the same expression for the tails case.

That has been the equivalent of an Exxon Valdez spill every year since 1969.

For any coin, with the probability of heads equals to all caps P,. we now get the following formula n! (n k)! k!.

He's beginning to talk about his past mistakes, something about a Stafford job that backfired.