00:01
Okay, we are told that 81 % of people in court are actually guilty.
00:06
So, this is a tree diagram for this.
00:09
Here is guilty, here is not guilty.
00:14
So, there's a 0 .81 chance they are guilty.
00:19
Which means not guilty is a 0 .19 chance, 1 minus .81.
00:25
For tree diagrams, each branch must add up to give me 1.
00:30
Now, if you are guilty, the chance you're convicted, so c for convicted, is 0 .91, which means the chance you're acquitted, that's a, is 1 minus that, so a very small chance, 0 .09, that you are guilty, but you're found not guilty, you're acquitted.
00:56
Now, if you're not guilty, then acquitted becomes 0 .9.
01:04
Which means you're convicted wrongly 0 .09 of the time.
01:14
So not guilty but you are found guilty .09.
01:19
We are told the defendant is convicted.
01:23
Let's work out then the branch that contains convicted, which is here and here.
01:30
This one is 0 .81 times 0 .91 for being guilty and convicted.
01:37
That i work out on a calculator and that is 0 .7371.
01:52
Now down here, 0 .19 times 0 .09 is not guilty and convicted.
02:00
So 0 .19 times 0 .09 that will be equal to 0 .1171.
02:18
Now, we know for a fact that the person was convicted, so my sample space will be these two numbers in green added up.
02:32
So, 0 .111 plus 0 .7171 is 0 .7171 is 0 .7542.
02:48
Now, i want to work out p of innocent, so p of not guilty, given you are convicted.
03:05
That line means given that.
03:08
So that means my sample space is .7542, i .e.
03:16
This number here, convicted in total.
03:19
And what i want is the not guilty one, which is this one here, from here.
03:25
So on top then we'll go 0 .1171.
03:32
So please more chance.
03:34
So 0 .1171 divided by 0 .7542 is 0 .0267...