00:01
Okay, we have here two urns, a and b.
00:04
A contains five red, three white, b contains one red and two white.
00:10
A dye is thrown.
00:11
It says eight or six.
00:13
I'm guessing here's a misprint should be three or six.
00:16
If that appears, a ball is drawn from b and put in a.
00:21
So getting a three or a six then is going to be two chances out of six.
00:27
You throw a dye, there are six outcomes possible.
00:30
That's your sample space.
00:31
Two of them are three or six and the other would be four chances out of six.
00:37
In other words, getting a one, two, four or five.
00:41
Now if we get a three or a six, what happens? go to earn b and take out a ball.
00:53
So we're now at earn b and i take out either a red ball or a white ball.
01:01
Now red is going to be one chance out of three.
01:07
There are three balls in there in b.
01:10
One is red.
01:11
White, two out of three.
01:15
And then that ball is put into a.
01:19
So what happens now is we have burn a, which now contains six red, one more than five over here, and still contains three white.
01:35
And then we take out a ball from here at random, which could be red, it could be white.
01:42
There are nine balls now in urn a, so six are red, so six out of nine, and three are white, so three out of nine.
01:54
Okay, that's that one done.
01:58
The next one here, same idea.
02:01
We're still with earn a, but i'm now adding a white.
02:06
So what's happening here is there are still 5 red, but now we're up to 4 white.
02:15
And then again take out one more.
02:18
On earn a, could be red, could be white.
02:23
Red is 5 chances out of 9, and white now is 4 out of 9.
02:31
Okay, the other case, we go to earn a and take out a ball, a marble.
02:43
It could be red, let's get it down here, messy here, it could be red, it could be white, from urn a.
02:54
Getting a red from earn a is five out of eight, eight balls, and five are red.
03:03
So here then, it will be five out of eight, and here three out of eight.
03:09
Then a ball is put into urn b, which means urn b now contains set of one red, two white, two red, two white.
03:24
We have two red here and two white.
03:30
And then if we get a white ball here, again that goes to urn b, and there will now be one red skill, but now three white.
03:45
And last of all, then we take out one ball from b, and that could be red or white.
03:53
Red is two out of four, white two out of four.
03:57
And down here, red, white, one chance out of four for red, three out of four for white.
04:08
Okay, that's my complete three diagram.
04:11
Now i want to work out first, a, b of both balls are red.
04:27
So, look at my tree diagram.
04:30
Let's find where they're both going to be red.
04:33
Well, red comes out here, red comes out here.
04:39
So i've worked out that particular branch, which will be two out of six times one out of three times six out of nine.
04:49
So we get here this branch two out of six times one out of three times six out of nine.
05:02
2, 6, 1 3rd, 6 .9.
05:05
And that i work out.
05:08
And we have here, the 6th here and 6 here cancel out...