00:01
So we have a question here for rolling dice.
00:03
In part a, we are rolling two dice, or rather a dice twice, and we're looking at the sum of the numbers.
00:10
So i'm going to have roll a and roll b.
00:13
Now on each of these, there are six different outcomes, anything from one to six.
00:23
So if i want to look at what i got on the dice as a, b, there are 36 outcomes here.
00:32
I can get 36 strings of first, second.
00:36
Because there are six for a, there are six for b.
00:40
Multiply that, 36.
00:41
And because these are fair, each outcome is equally likely, these 36 outcomes are all equally likely as well.
00:48
Each is one in 36.
00:50
Now i'm going to look at the different sums we might get.
00:53
We could get 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12.
01:01
And to find the probabilities for these, i'm going to look at how many of my 36 outcomes would get that sum.
01:07
For example, if we look at 2, there's only one way to make that happen.
01:10
1, 1.
01:11
So this has a 1 in 36 chance.
01:16
12 is also 1 in 36.
01:19
You have to get 6, 6.
01:22
3 could be 1, 2, or 2, 1.
01:24
That's 2 out of 36.
01:27
11 could be 5, 6, or 6, 5.
01:30
2 out of 36.
01:32
You can see some symmetry going on here.
01:34
4 would be 1, 3, 3, 1, or 2, 2.
01:37
So 3 out of 36.
01:40
And 10 is 3 out of 36 as well.
01:42
4, 6, 6, 4, 5, 5.
01:45
5 is 1, 4, 4, 1, 2, 3, or 3, 2.
01:49
That's 4 outcomes out of 36.
01:53
And keeping up the symmetry over here, 6 could be 1, 5, 5, 1, 2, 4, 4, 2, 3, 3.
02:00
So 5 outcomes.
02:01
Outcomes.
02:03
Same for 8.
02:06
And finally 7 is the remaining 6 outcomes.
02:09
1, 6, 6, 1, 2, 5, 5, 2, 3, 4, 4, 3.
02:14
And if you wanted to check, if you add these up, the probabilities do add up to 36 out of 36, since we've got all the outcomes accounted for, which is 1, as it should be...