[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.83,0:00:02.24,Default,,0000,0000,0000,,Well, let's talk for the last video.
Dialogue: 0,0:00:02.24,0:00:04.30,Default,,0000,0000,0000,,We were saying, well I have two dices,
Dialogue: 0,0:00:04.30,0:00:06.82,Default,,0000,0000,0000,,like you know we're playing monopoly with two six sided dice
Dialogue: 0,0:00:06.82,0:00:08.67,Default,,0000,0000,0000,,and I want to say what is the probability that I will get a 7?
Dialogue: 0,0:00:08.67,0:00:12.10,Default,,0000,0000,0000,,So when I add up the two rows of the dice
Dialogue: 0,0:00:12.10,0:00:13.14,Default,,0000,0000,0000,,was the probablity I get 7.
Dialogue: 0,0:00:13.14,0:00:16.19,Default,,0000,0000,0000,,So I drew this grid here:and this grid esentially represents
Dialogue: 0,0:00:16.67,0:00:18.87,Default,,0000,0000,0000,,all of the outcomes that I could get with the two dice
Dialogue: 0,0:00:19.18,0:00:23.24,Default,,0000,0000,0000,,where on the top row that is the outcomes on dice 1 that
Dialogue: 0,0:00:23.24,0:00:25.58,Default,,0000,0000,0000,,I can get a 1, a 2, a 3, a 4, a 5, or a 6
Dialogue: 0,0:00:25.58,0:00:27.51,Default,,0000,0000,0000,,and similarly for dice two these are all of the outcomes
Dialogue: 0,0:00:27.51,0:00:27.95,Default,,0000,0000,0000,,that I could get.
Dialogue: 0,0:00:27.95,0:00:32.35,Default,,0000,0000,0000,,So each of these squares represents a particular outcome of both dices.
Dialogue: 0,0:00:32.35,0:00:34.07,Default,,0000,0000,0000,,For example, this square means
Dialogue: 0,0:00:34.07,0:00:37.91,Default,,0000,0000,0000,,that I got 6 on dice 1 and 6 on dice 2, right?
Dialogue: 0,0:00:38.49,0:00:40.47,Default,,0000,0000,0000,,And of course, what does it mean that they added up to,
Dialogue: 0,0:00:40.47,0:00:42.94,Default,,0000,0000,0000,,they added up to 12, right?
Dialogue: 0,0:00:43.22,0:00:44.26,Default,,0000,0000,0000,,And we can go through all of them.
Dialogue: 0,0:00:44.26,0:00:46.49,Default,,0000,0000,0000,,we could take some dice 1, dice 2,
Dialogue: 0,0:00:46.49,0:00:47.76,Default,,0000,0000,0000,,well we see what they added up to?
Dialogue: 0,0:00:48.07,0:00:54.89,Default,,0000,0000,0000,,Well, this is 2. This is 3,4,5,6,7.
Dialogue: 0,0:00:55.27,0:00:58.02,Default,,0000,0000,0000,,And then this will be 3, let's go up it.
Dialogue: 0,0:00:58.02,0:00:59.18,Default,,0000,0000,0000,,Let's see, this will be 3.
Dialogue: 0,0:00:59.18,0:01:05.34,Default,,0000,0000,0000,,Then whis will be 4,5,6,7,8.
Dialogue: 0,0:01:05.61,0:01:07.73,Default,,0000,0000,0000,,This will be, let's do all of them, 4,
Dialogue: 0,0:01:07.99,0:01:12.93,Default,,0000,0000,0000,,and let's keep going on, 5,6,7,8,9.
Dialogue: 0,0:01:13.25,0:01:19.59,Default,,0000,0000,0000,,This was 4 plus 1. This is 5,6,7,8,9,10.
Dialogue: 0,0:01:19.59,0:01:21.68,Default,,0000,0000,0000,,And I think this is still an interesting pattern here, right?
Dialogue: 0,0:01:21.68,0:01:28.13,Default,,0000,0000,0000,,This would be 6,7,8,9,10,11.
Dialogue: 0,0:01:28.13,0:01:33.20,Default,,0000,0000,0000,,And this is 7,8,9,10,11,12.
Dialogue: 0,0:01:33.53,0:01:36.22,Default,,0000,0000,0000,,So if I said, what is the probablity of getting a 7?
Dialogue: 0,0:01:36.51,0:01:39.17,Default,,0000,0000,0000,,Well, that's all the squares that have a 7 item.
Dialogue: 0,0:01:39.17,0:01:41.45,Default,,0000,0000,0000,,So let's see, that is, let me see if you can use this.
Dialogue: 0,0:01:41.66,0:01:43.68,Default,,0000,0000,0000,,This fills to, that will be interesting.
Dialogue: 0,0:01:43.90,0:01:50.26,Default,,0000,0000,0000,,So all the sevens, this one, this one, this one, this one,
Dialogue: 0,0:01:50.46,0:01:52.52,Default,,0000,0000,0000,,this one, that one.
Dialogue: 0,0:01:52.78,0:01:54.33,Default,,0000,0000,0000,,So what's the probability that I can get
Dialogue: 0,0:01:54.33,0:01:55.98,Default,,0000,0000,0000,,actually I can try pretty neat that it will work.
Dialogue: 0,0:01:56.21,0:01:57.88,Default,,0000,0000,0000,,What's the probablity of getting 7?
Dialogue: 0,0:01:57.88,0:02:02.17,Default,,0000,0000,0000,,Well as we from our original definitions of the probability.
Dialogue: 0,0:02:02.17,0:02:05.52,Default,,0000,0000,0000,,What is the total number equally, let me do it here.
Dialogue: 0,0:02:05.52,0:02:06.71,Default,,0000,0000,0000,,Probability of 7.
Dialogue: 0,0:02:07.02,0:02:10.33,Default,,0000,0000,0000,,What's the total number of equally probable outcomes?
Dialogue: 0,0:02:10.60,0:02:14.08,Default,,0000,0000,0000,,We have 36 outcomes, since these are all equally probable, right?
Dialogue: 0,0:02:14.33,0:02:16.45,Default,,0000,0000,0000,,There is 36 total out outcomes.
Dialogue: 0,0:02:16.71,0:02:18.26,Default,,0000,0000,0000,,And so what's the probability of getting 7?
Dialogue: 0,0:02:18.26,0:02:23.79,Default,,0000,0000,0000,,How many of these 36 outcomes resulted in the dice out of getting 7?
Dialogue: 0,0:02:24.07,0:02:28.45,Default,,0000,0000,0000,,That's 1,2,3,4,5,6, so 6.
Dialogue: 0,0:02:28.81,0:02:37.15,Default,,0000,0000,0000,,The probablity of getting a 7 is equal to 6 over 36 is equally 1/6.
Dialogue: 0,0:02:37.65,0:02:40.33,Default,,0000,0000,0000,,So we could, you know, use this great useful
Dialogue: 0,0:02:40.33,0:02:42.19,Default,,0000,0000,0000,,for the probability of getting any number.
Dialogue: 0,0:02:42.47,0:02:45.07,Default,,0000,0000,0000,,We could say, and we could even, just by looking at this.
Dialogue: 0,0:02:45.07,0:02:48.93,Default,,0000,0000,0000,,We see the most likely of all of the numbers you get 7, right?
Dialogue: 0,0:02:49.20,0:02:50.64,Default,,0000,0000,0000,,And if you just look at the pattern,
Dialogue: 0,0:02:50.86,0:02:54.88,Default,,0000,0000,0000,,cause it covers the whole diaconal, in terms of, and then you know,
Dialogue: 0,0:02:55.06,0:02:57.85,Default,,0000,0000,0000,,the probablity of getting a 6 is equal to the probablity of getting 8,
Dialogue: 0,0:02:58.29,0:02:59.36,Default,,0000,0000,0000,,you know, the probablity of getting 9
Dialogue: 0,0:02:59.36,0:03:05.75,Default,,0000,0000,0000,,that is equal to the probablity of getting a 5 and so forth.
Dialogue: 0,0:03:05.75,0:03:08.70,Default,,0000,0000,0000,,Let's do that. Let's see so 7 is the most probable
Dialogue: 0,0:03:08.98,0:03:11.94,Default,,0000,0000,0000,,and just get some intonation on dice rows.
Dialogue: 0,0:03:12.62,0:03:15.76,Default,,0000,0000,0000,,Let's see what's the socond line?
Dialogue: 0,0:03:15.76,0:03:16.87,Default,,0000,0000,0000,,What's the probablity of getting 8?
Dialogue: 0,0:03:16.87,0:03:22.25,Default,,0000,0000,0000,,8,8,8,8,8.
Dialogue: 0,0:03:22.53,0:03:26.11,Default,,0000,0000,0000,,So how many 8s are there out of the total number?
Dialogue: 0,0:03:27.22,0:03:31.15,Default,,0000,0000,0000,,Let's see, so the probability of getting an 8
Dialogue: 0,0:03:32.24,0:03:36.97,Default,,0000,0000,0000,,is equal to 1,2,3,4,5, is equal to 5 over 36.
Dialogue: 0,0:03:37.23,0:03:39.30,Default,,0000,0000,0000,,And that's also equal to probablity of getting a 6, right?
Dialogue: 0,0:03:39.52,0:03:45.94,Default,,0000,0000,0000,,1,2,3,4,5,6, probablity of getting a 6.
Dialogue: 0,0:03:45.94,0:03:49.41,Default,,0000,0000,0000,,So let me call this sixes as the same green,
Dialogue: 0,0:03:49.41,0:03:55.53,Default,,0000,0000,0000,,just so we know that's 6.
Dialogue: 0,0:03:55.53,0:03:57.18,Default,,0000,0000,0000,,So those all the sixes.
Dialogue: 0,0:03:57.40,0:03:59.11,Default,,0000,0000,0000,,And this actually wouldn't hurt to memorize
Dialogue: 0,0:03:59.11,0:04:00.89,Default,,0000,0000,0000,,cause when you play a noply you know you are,
Dialogue: 0,0:04:00.89,0:04:03.21,Default,,0000,0000,0000,,you know, landing on board work for example.
Dialogue: 0,0:04:03.21,0:04:07.62,Default,,0000,0000,0000,,Then you'd have to, you know,
Dialogue: 0,0:04:08.34,0:04:11.95,Default,,0000,0000,0000,,actually I'll probablity do another video on what expected value
Dialogue: 0,0:04:12.24,0:04:13.90,Default,,0000,0000,0000,,and expected cost of things like that
Dialogue: 0,0:04:13.90,0:04:15.87,Default,,0000,0000,0000,,cause the probability costed a little of money
Dialogue: 0,0:04:15.87,0:04:17.60,Default,,0000,0000,0000,,that will be very useful when you play a noply.
Dialogue: 0,0:04:17.98,0:04:21.83,Default,,0000,0000,0000,,And so we can keep doing what's the probability of 5 was 1,2,3,4.
Dialogue: 0,0:04:22.19,0:04:24.65,Default,,0000,0000,0000,,There is four out of the 36 outcomes of 5.
Dialogue: 0,0:04:24.97,0:04:31.97,Default,,0000,0000,0000,,The probablity of 5 is 4/36, and that is equal 1/9.
Dialogue: 0,0:04:31.97,0:04:33.80,Default,,0000,0000,0000,,And that's also the same as the probablity of getting a 9,
Dialogue: 0,0:04:35.39,0:04:36.86,Default,,0000,0000,0000,,probability 9 is 1/9.
Dialogue: 0,0:04:37.29,0:04:39.50,Default,,0000,0000,0000,,So that's interesting, I mean you know if you are play the crabs
Dialogue: 0,0:04:39.50,0:04:42.23,Default,,0000,0000,0000,,or the thing monoply, you now have a sense of
Dialogue: 0,0:04:42.45,0:04:44.59,Default,,0000,0000,0000,,what the different probabilities are of the different rows.
Dialogue: 0,0:04:44.82,0:04:47.05,Default,,0000,0000,0000,,And you know, that's why I think a lot of games,
Dialogue: 0,0:04:47.25,0:04:48.84,Default,,0000,0000,0000,,you know 7 is very important row,
Dialogue: 0,0:04:49.04,0:04:53.51,Default,,0000,0000,0000,,because that is, actually the most probable of number.
Dialogue: 0,0:04:53.51,0:04:56.51,Default,,0000,0000,0000,,For example, the probability of getting a 7 is higher
Dialogue: 0,0:04:56.66,0:05:02.92,Default,,0000,0000,0000,,than the probability of getting a 9 or a 5, right?
Dialogue: 0,0:05:02.92,0:05:11.05,Default,,0000,0000,0000,,Cause what's the probability of a 5 or a 9, that U is or, right?
Dialogue: 0,0:05:11.05,0:05:13.22,Default,,0000,0000,0000,,Well, that's the probability of getting a 5
Dialogue: 0,0:05:13.48,0:05:15.82,Default,,0000,0000,0000,,plus the probability of getting a 9
Dialogue: 0,0:05:16.04,0:05:23.28,Default,,0000,0000,0000,,which is equal 1/9 plus 1/9 which is equal to 2/9,
Dialogue: 0,0:05:23.28,0:05:24.28,Default,,0000,0000,0000,,or actually I was wrong,.
Dialogue: 0,0:05:24.47,0:05:26.80,Default,,0000,0000,0000,,You see, that's why it could do a calculation.
Dialogue: 0,0:05:27.01,0:05:29.90,Default,,0000,0000,0000,,1/6 is less than 2/9.
Dialogue: 0,0:05:29.90,0:05:31.45,Default,,0000,0000,0000,,So this is a higher one.
Dialogue: 0,0:05:31.45,0:05:33.65,Default,,0000,0000,0000,,But I can't see so I was wrong about that.
Dialogue: 0,0:05:33.65,0:05:39.04,Default,,0000,0000,0000,,We can see the probability of getting a, let's see,
Dialogue: 0,0:05:39.04,0:05:49.84,Default,,0000,0000,0000,,a 2 or 11, is less than the probability of getting a 7.
Dialogue: 0,0:05:50.12,0:05:52.20,Default,,0000,0000,0000,,Let's calculate that. What's the probability of getting a 2?
Dialogue: 0,0:05:52.45,0:05:56.64,Default,,0000,0000,0000,,Actually I should say a 3 or a 11.
Dialogue: 0,0:05:56.64,0:05:58.35,Default,,0000,0000,0000,,I wanted it to be special or 6 that I wrote.
Dialogue: 0,0:05:58.35,0:06:00.31,Default,,0000,0000,0000,,Probability of 2, there is only 1 situation
Dialogue: 0,0:06:00.31,0:06:01.19,Default,,0000,0000,0000,,where I can get a 2, right?
Dialogue: 0,0:06:01.44,0:06:06.18,Default,,0000,0000,0000,,So this is 1/36, 1 over 36 is 2.
Dialogue: 0,0:06:06.45,0:06:08.88,Default,,0000,0000,0000,,And 11, that's 2 out of 36, right?
Dialogue: 0,0:06:09.15,0:06:15.07,Default,,0000,0000,0000,,So 2 out of 36 is 1/18. Let me write this to 2/36.
Dialogue: 0,0:06:15.41,0:06:20.39,Default,,0000,0000,0000,,So that equals 3/36. So that equals 1/12.
Dialogue: 0,0:06:20.71,0:06:22.89,Default,,0000,0000,0000,,So the probability of getting a 2 which is this one,
Dialogue: 0,0:06:22.89,0:06:26.74,Default,,0000,0000,0000,,or 11 is 1 out of 12 or the probability of getting,
Dialogue: 0,0:06:26.74,0:06:31.08,Default,,0000,0000,0000,,so the probability of getting a 7 is twice than of getting a 2 or 11.
Dialogue: 0,0:06:31.08,0:06:32.82,Default,,0000,0000,0000,,So let's just interesting out of, you know,
Dialogue: 0,0:06:32.82,0:06:34.07,Default,,0000,0000,0000,,sometimes I don't knoe where is this going.
Dialogue: 0,0:06:34.07,0:06:35.78,Default,,0000,0000,0000,,But I think it's interesting to analyse dice
Dialogue: 0,0:06:35.78,0:06:37.43,Default,,0000,0000,0000,,because dice show up a lot.
Dialogue: 0,0:06:38.44,0:06:40.75,Default,,0000,0000,0000,,And another way, although this green is
Dialogue: 0,0:06:40.75,0:06:42.71,Default,,0000,0000,0000,,probably declears way of doing it.
Dialogue: 0,0:06:43.31,0:06:47.57,Default,,0000,0000,0000,,Another way that I do it, if I don't have a green in front of mne.
Dialogue: 0,0:06:47.57,0:06:50.32,Default,,0000,0000,0000,,If I say, what is the probability of getting a,
Dialogue: 0,0:06:50.62,0:06:53.53,Default,,0000,0000,0000,,I don't know, let's say what's the probability of getting a 5.
Dialogue: 0,0:06:54.80,0:06:58.17,Default,,0000,0000,0000,,Well, it's the probability of, let's say, this is dice 1.
Dialogue: 0,0:06:58.44,0:07:00.37,Default,,0000,0000,0000,,And this is essencially the same thing as grid but it's
Dialogue: 0,0:07:00.37,0:07:03.49,Default,,0000,0000,0000,,good to have mortal free work of this.
Dialogue: 0,0:07:03.79,0:07:04.89,Default,,0000,0000,0000,,So, how can I get a 5?
Dialogue: 0,0:07:04.89,0:07:11.23,Default,,0000,0000,0000,,If I get a 1 on dice 1, I get a 4 on dice 2.
Dialogue: 0,0:07:11.51,0:07:13.18,Default,,0000,0000,0000,,If I get a 2, and then I need a 3.
Dialogue: 0,0:07:13.18,0:07:15.05,Default,,0000,0000,0000,,If I get a 3, then I need a 2.
Dialogue: 0,0:07:15.36,0:07:19.23,Default,,0000,0000,0000,,If I have a 4, then I need a 1.
Dialogue: 0,0:07:19.24,0:07:22.14,Default,,0000,0000,0000,,And if I have a 5, no.
Dialogue: 0,0:07:22.39,0:07:24.67,Default,,0000,0000,0000,,Those are only the stuations, right?
Dialogue: 0,0:07:24.90,0:07:28.40,Default,,0000,0000,0000,,So we could say, what's the probability of getting, so this,
Dialogue: 0,0:07:28.61,0:07:30.23,Default,,0000,0000,0000,,we need each of these probabilities,
Dialogue: 0,0:07:30.23,0:07:31.85,Default,,0000,0000,0000,,and then the next one has to be this.
Dialogue: 0,0:07:32.39,0:07:37.15,Default,,0000,0000,0000,,So there is 4 probabilities that kind of keeping this game in dice 1.
Dialogue: 0,0:07:37.15,0:07:38.35,Default,,0000,0000,0000,,So that's the probability of getting 1?
Dialogue: 0,0:07:38.35,0:07:40.33,Default,,0000,0000,0000,,That's 1/6. This is dice 1.
Dialogue: 0,0:07:41.71,0:07:47.32,Default,,0000,0000,0000,,This is, you get a 2, 3. This is you get 4, right?
Dialogue: 0,0:07:47.32,0:07:49.34,Default,,0000,0000,0000,,And so what's the probability of getting 1 on dice 1?
Dialogue: 0,0:07:49.57,0:07:53.00,Default,,0000,0000,0000,,It's 1/6, right? They are all 1/6.
Dialogue: 0,0:07:53.00,0:07:54.03,Default,,0000,0000,0000,,That's the probability of getting 2.
Dialogue: 0,0:07:54.15,0:07:55.23,Default,,0000,0000,0000,,That's the probability of getting 3.
Dialogue: 0,0:07:55.35,0:07:57.39,Default,,0000,0000,0000,,That's the probability of getting 4, right?
Dialogue: 0,0:07:57.52,0:08:00.76,Default,,0000,0000,0000,,And so, even if a 1 on dice 1,
Dialogue: 0,0:08:00.76,0:08:02.01,Default,,0000,0000,0000,,what's the probability of getting 4 then?
Dialogue: 0,0:08:03.33,0:08:05.45,Default,,0000,0000,0000,,So then you know, there is 6 probabilities, and you know,
Dialogue: 0,0:08:05.45,0:08:07.17,Default,,0000,0000,0000,,there is a tree, you can get a 5 or 6,
Dialogue: 0,0:08:07.17,0:08:09.10,Default,,0000,0000,0000,,but those aren't count because we are out of the game.
Dialogue: 0,0:08:09.35,0:08:12.93,Default,,0000,0000,0000,,So dice 1 and then on dice 2 there is one out of 6 chance
Dialogue: 0,0:08:12.93,0:08:13.79,Default,,0000,0000,0000,,so I can get a 4.
Dialogue: 0,0:08:13.98,0:08:16.53,Default,,0000,0000,0000,,Then there is, you know, about the other chance of the other number.
Dialogue: 0,0:08:16.53,0:08:20.00,Default,,0000,0000,0000,,But this is the only situation we get a 5, right?
Dialogue: 0,0:08:20.33,0:08:24.09,Default,,0000,0000,0000,,Similarly, on dice, this is dice 2, this column.
Dialogue: 0,0:08:24.63,0:08:26.30,Default,,0000,0000,0000,,And then, if I get a 2,
Dialogue: 0,0:08:26.30,0:08:27.45,Default,,0000,0000,0000,,what do I need on dice 2?
Dialogue: 0,0:08:27.45,0:08:31.39,Default,,0000,0000,0000,,I need a 3, but to get exactly a 3, there is 1/6 chance again.
Dialogue: 0,0:08:31.62,0:08:33.64,Default,,0000,0000,0000,,And of course, this is 5.
Dialogue: 0,0:08:33.91,0:08:37.06,Default,,0000,0000,0000,,I have a 3 here, then there 1/6 chance that I get a 2,
Dialogue: 0,0:08:37.34,0:08:38.65,Default,,0000,0000,0000,,which is exactly what I need.
Dialogue: 0,0:08:38.88,0:08:40.31,Default,,0000,0000,0000,,And of course, there is a lot of the other things
Dialogue: 0,0:08:40.31,0:08:41.95,Default,,0000,0000,0000,,that you can get that we are selecting for the 5s.
Dialogue: 0,0:08:42.24,0:08:44.45,Default,,0000,0000,0000,,And if I had a 4, I am going to switch colors.
Dialogue: 0,0:08:44.78,0:08:50.27,Default,,0000,0000,0000,,There is 1/6 chance that I get a 1 to get a 5, right?
Dialogue: 0,0:08:50.55,0:08:52.01,Default,,0000,0000,0000,,So what are all the probabilities of these?
Dialogue: 0,0:08:52.01,0:08:53.59,Default,,0000,0000,0000,,Well, this is 1/6 times ones.
Dialogue: 0,0:08:53.59,0:08:57.59,Default,,0000,0000,0000,,So the probability of this. of getting a 1 and then a 4.
Dialogue: 0,0:08:58.22,0:09:03.76,Default,,0000,0000,0000,,Let me clean this up. I am running out of time.
Dialogue: 0,0:09:04.94,0:09:07.26,Default,,0000,0000,0000,,Actually, let me do it on this side.
Dialogue: 0,0:09:07.61,0:09:15.33,Default,,0000,0000,0000,,So the probability of this event, these are mess and normal,
Dialogue: 0,0:09:15.60,0:09:18.12,Default,,0000,0000,0000,,of this one, of getting 1 and then getting a 4,
Dialogue: 0,0:09:18.42,0:09:21.22,Default,,0000,0000,0000,,well that's 1/36, right?
Dialogue: 0,0:09:21.22,0:09:24.69,Default,,0000,0000,0000,,1/6, this is 1/6 times 1/6.
Dialogue: 0,0:09:24.69,0:09:27.10,Default,,0000,0000,0000,,This is 1/6 then after that happened you could another 1/6.
Dialogue: 0,0:09:27.10,0:09:30.13,Default,,0000,0000,0000,,That's 1/36 by similar logic.
Dialogue: 0,0:09:30.13,0:09:34.65,Default,,0000,0000,0000,,This is 1/36, this is 1/36, and this is 1/36.
Dialogue: 0,0:09:34.96,0:09:38.19,Default,,0000,0000,0000,,Each of these 1/36, and you think about that grid we drew,
Dialogue: 0,0:09:38.19,0:09:40.78,Default,,0000,0000,0000,,each of these outcomes represent a square on that grid
Dialogue: 0,0:09:41.07,0:09:43.54,Default,,0000,0000,0000,,getting a 2 and get a 3, getting a 1 and then getiing 4.
Dialogue: 0,0:09:43.76,0:09:46.72,Default,,0000,0000,0000,,And then our total probability of getiing 5 is some of all this.
Dialogue: 0,0:09:46.72,0:09:49.38,Default,,0000,0000,0000,,4/36 which is equal to 1/9.
Dialogue: 0,0:09:49.63,0:09:51.62,Default,,0000,0000,0000,,So that's one that you don't have to draw a grid.
Dialogue: 0,0:09:52.15,0:09:54.14,Default,,0000,0000,0000,,You could do a tree. You could do a little table like this
Dialogue: 0,0:09:54.14,0:09:56.07,Default,,0000,0000,0000,,and say what are the ways that I can get a 5
Dialogue: 0,0:09:56.07,0:09:58.41,Default,,0000,0000,0000,,and what's the probability of each of these, then some one up.
Dialogue: 0,0:09:58.41,0:10:01.05,Default,,0000,0000,0000,,And they all work and in different times
Dialogue: 0,0:10:01.05,0:10:04.30,Default,,0000,0000,0000,,different methods would be more useful.
Dialogue: 0,0:10:04.68,0:10:06.29,Default,,0000,0000,0000,,I will see you in the next video.