00:01
Okay, we are told a coin is biased so that the head is twice as likely as a tail.
00:06
So the ratio between head and tail then is 2 to 1, which means p of getting a head must be 2 out of 3, 2 thirds, and p of getting a tail must be 1 third.
00:23
The sum must be 1, which it is, and you can see 2 thirds is twice 1 third.
00:29
I want to work out the distribution of heads.
00:35
So a table then like this.
00:37
Here is x.
00:39
You could have no heads, one head, two heads, or three heads.
00:46
I throw the coin three times.
00:52
Here is p of x equals x.
00:59
So x then equals number of heads.
01:07
So let's work out each one.
01:12
First one then is no heads.
01:14
Well, p of no heads means i get three tails.
01:19
So, p of three tails would be one third times one third times one third.
01:30
So one third power three, which is going to be one over 27.
01:37
That will be chance of getting no heads.
01:42
Now, p of exactly one head.
01:49
So one head, two tails.
01:53
That will be two thirds for the head.
01:57
One third squared for two tails.
02:01
And that we can do more than one way.
02:03
You can do it three ways, in fact.
02:05
The head could occur first or second or third coin throw...