00:01
Okay, we have here an urn containing eight white, four black and two orange balls.
00:07
Take out two balls are random.
00:09
Every black one you take out, you win two dollars.
00:12
Every white one you'll lose one dollar and orange has no effect.
00:17
Let's work out first then what could happen.
00:20
We have here a total of 14 balls so far.
00:25
Well, 14 balls.
00:27
It's my sample space to begin with.
00:29
And what could happen? i could have white followed by white, white followed by black, white followed by orange.
00:40
Then it could be black followed by white, black followed by black, black followed by orange.
00:50
Then it could be orange followed by white, orange followed by black, orange followed by orange.
00:57
And each one of these have to work out.
01:01
So the chance of getting white followed by white will be 8 out of 14 to get a white ball on the first choice and then 7 out of 13 for number 2.
01:20
So that will be 56 over 14 times 13 is 182.
01:31
Now to get white first, again, 8 out of 14.
01:36
Black second, other of 4 black.
01:38
So 4 out of 13.
01:41
8 times 4, 32 out of 1, 82.
01:46
Now white, again 8 out of 14.
01:50
Orange will be 2 out of 13.
01:53
So we have 16 here out of 1, 82.
01:57
That's the first 3 done.
02:00
Okay, the next one then.
02:02
Black first will be four out of 14 white second will be eight out of 13 so we get here 32 over 1 8 8 2 black first 4 out of 14 black second 3 out of 13 so 12 out of 1 8 2 black first 4 out of 14 orange second, two out of 13.
02:34
So eight out of one, eight, two.
02:39
Then, orange first, two chances from 14.
02:44
White, eight chances from 13.
02:47
16 over 1, 82.
02:51
Orange first, 2 out of 14.
02:54
Black second, 4 out of 13 will be 8 over 1, 82.
03:00
The last one, two out of 14, 1 out of 13, will be 2 out of 1, 8, 2.
03:09
Okay, these fractions do not simplify as fine as they are.
03:16
Okay, now let's work out next how much we win in each case or lose.
03:26
So, i come to here.
03:28
We are told that if you choose a white ball, you will lose $1.
03:33
So up here then the first one, white followed by white, i'm going to lose.
03:41
Let's say here we have a column of winnings.
03:47
Here i'm going to lose $2.
03:57
So white followed by white minus two.
04:00
Now white followed by black.
04:03
White i will lose one, but black i'll win two.
04:06
So overall i am plus one.
04:09
Now white followed by orange, white i will lose $1.
04:15
So that will be minus one...