[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.64,0:00:02.97,Default,,0000,0000,0000,,Let's do a little bit of\Nprobability with playing cards.
Dialogue: 0,0:00:02.97,0:00:04.51,Default,,0000,0000,0000,,And for the sake of\Nthis video, we're
Dialogue: 0,0:00:04.51,0:00:06.86,Default,,0000,0000,0000,,going to assume that our\Ndeck has no jokers in it.
Dialogue: 0,0:00:06.86,0:00:08.78,Default,,0000,0000,0000,,You could do the same\Nproblems with the joker,
Dialogue: 0,0:00:08.78,0:00:11.56,Default,,0000,0000,0000,,you'll just get slightly\Ndifferent numbers.
Dialogue: 0,0:00:11.56,0:00:13.39,Default,,0000,0000,0000,,So with that out of\Nthe way, let's first
Dialogue: 0,0:00:13.39,0:00:15.80,Default,,0000,0000,0000,,just think about\Nhow many cards we
Dialogue: 0,0:00:15.80,0:00:18.21,Default,,0000,0000,0000,,have in a standard playing deck.
Dialogue: 0,0:00:18.21,0:00:23.04,Default,,0000,0000,0000,,So you have four\Nsuits, and the suits
Dialogue: 0,0:00:23.04,0:00:26.96,Default,,0000,0000,0000,,are the spades, the diamonds,\Nthe clubs, and the hearts.
Dialogue: 0,0:00:26.96,0:00:29.77,Default,,0000,0000,0000,,You have four suits and\Nthen in each of those suits
Dialogue: 0,0:00:29.77,0:00:31.95,Default,,0000,0000,0000,,you have 13 different\Ntypes of cards--
Dialogue: 0,0:00:31.95,0:00:33.64,Default,,0000,0000,0000,,and sometimes it's\Ncalled the rank.
Dialogue: 0,0:00:43.97,0:00:47.92,Default,,0000,0000,0000,,You have the ace, then you have\Nthe two, the three, the four,
Dialogue: 0,0:00:47.92,0:00:52.21,Default,,0000,0000,0000,,the five, the six,\Nseven, eight, nine, ten,
Dialogue: 0,0:00:52.21,0:00:55.62,Default,,0000,0000,0000,,and then you have the Jack,\Nthe King, and the Queen.
Dialogue: 0,0:00:55.62,0:00:57.59,Default,,0000,0000,0000,,And that is 13 cards.
Dialogue: 0,0:00:57.59,0:01:00.89,Default,,0000,0000,0000,,So for each suit\Nyou can have any
Dialogue: 0,0:01:00.89,0:01:03.48,Default,,0000,0000,0000,,of these-- you can\Nhave any of the suits.
Dialogue: 0,0:01:03.48,0:01:05.91,Default,,0000,0000,0000,,So you could have a Jack of\Ndiamonds, a Jack of clubs,
Dialogue: 0,0:01:05.91,0:01:09.22,Default,,0000,0000,0000,,a Jack of spades,\Nor a Jack of hearts.
Dialogue: 0,0:01:09.22,0:01:10.97,Default,,0000,0000,0000,,So if you just multiply\Nthese two things--
Dialogue: 0,0:01:10.97,0:01:13.53,Default,,0000,0000,0000,,you could take a deck of playing\Ncards, take out the jokers
Dialogue: 0,0:01:13.53,0:01:15.24,Default,,0000,0000,0000,,and count them-- but\Nif you just multiply
Dialogue: 0,0:01:15.24,0:01:18.74,Default,,0000,0000,0000,,this you have four suits, each\Nof those suits have 13 types.
Dialogue: 0,0:01:18.74,0:01:21.12,Default,,0000,0000,0000,,So you're going to\Nhave 4 times 13 cards,
Dialogue: 0,0:01:21.12,0:01:24.21,Default,,0000,0000,0000,,or you're going to have 52 cards\Nin a standard playing deck.
Dialogue: 0,0:01:24.21,0:01:25.79,Default,,0000,0000,0000,,Another way you could\Nhave said, look,
Dialogue: 0,0:01:25.79,0:01:28.27,Default,,0000,0000,0000,,there's 13 of these\Nranks, or types,
Dialogue: 0,0:01:28.27,0:01:31.12,Default,,0000,0000,0000,,and each of those come in four\Ndifferent suits-- 13 times 4.
Dialogue: 0,0:01:31.12,0:01:33.24,Default,,0000,0000,0000,,Once again, you would\Nhave gotten 52 cards.
Dialogue: 0,0:01:33.24,0:01:34.82,Default,,0000,0000,0000,,Now, with that of\Nthe way, let's think
Dialogue: 0,0:01:34.82,0:01:37.16,Default,,0000,0000,0000,,about the probabilities\Nof different events.
Dialogue: 0,0:01:37.16,0:01:38.53,Default,,0000,0000,0000,,So let's say I\Nshuffle that deck.
Dialogue: 0,0:01:38.53,0:01:40.61,Default,,0000,0000,0000,,I shuffle it really,\Nreally well and then
Dialogue: 0,0:01:40.61,0:01:43.24,Default,,0000,0000,0000,,I randomly pick a\Ncard from that deck.
Dialogue: 0,0:01:43.24,0:01:46.40,Default,,0000,0000,0000,,And I want to think about\Nwhat is the probability that I
Dialogue: 0,0:01:46.40,0:01:50.22,Default,,0000,0000,0000,,pick a Jack.
Dialogue: 0,0:01:50.22,0:01:53.45,Default,,0000,0000,0000,,Well, how many equally\Nlikely events are there?
Dialogue: 0,0:01:53.45,0:01:56.54,Default,,0000,0000,0000,,Well, I could pick any\None of those 52 cards.
Dialogue: 0,0:01:56.54,0:02:00.35,Default,,0000,0000,0000,,So there's 52 possibilities\Nfor when I pick that card.
Dialogue: 0,0:02:00.35,0:02:04.13,Default,,0000,0000,0000,,And how many of those 52\Npossibilities are Jacks?
Dialogue: 0,0:02:04.13,0:02:07.48,Default,,0000,0000,0000,,Well you have the Jack of\Nspades, the Jack of diamonds,
Dialogue: 0,0:02:07.48,0:02:09.88,Default,,0000,0000,0000,,the Jack of clubs, and\Nthe Jack of hearts.
Dialogue: 0,0:02:09.88,0:02:14.17,Default,,0000,0000,0000,,There's four Jacks in that deck.
Dialogue: 0,0:02:14.17,0:02:18.09,Default,,0000,0000,0000,,So it is 4 over 52-- these\Nare both divisible by 4-- 4
Dialogue: 0,0:02:18.09,0:02:23.06,Default,,0000,0000,0000,,divided by 4 is 1, 52\Ndivided by 4 is 13.
Dialogue: 0,0:02:23.06,0:02:27.39,Default,,0000,0000,0000,,Now, let's think\Nabout the probability.
Dialogue: 0,0:02:27.39,0:02:28.98,Default,,0000,0000,0000,,So I'll start over.
Dialogue: 0,0:02:28.98,0:02:30.60,Default,,0000,0000,0000,,I'm going to put that\NJack back and I'm
Dialogue: 0,0:02:30.60,0:02:31.85,Default,,0000,0000,0000,,going to reshuffle the deck.
Dialogue: 0,0:02:31.85,0:02:34.02,Default,,0000,0000,0000,,So once again, I\Nstill have 52 cards.
Dialogue: 0,0:02:34.02,0:02:37.29,Default,,0000,0000,0000,,So what's the probability\Nthat I get a hearts?
Dialogue: 0,0:02:37.29,0:02:39.29,Default,,0000,0000,0000,,What's the probability\Nthat I just randomly pick
Dialogue: 0,0:02:39.29,0:02:43.72,Default,,0000,0000,0000,,a card from a shuffled\Ndeck and it is a heart?
Dialogue: 0,0:02:43.72,0:02:46.58,Default,,0000,0000,0000,,Well, once again,\Nthere's 52 possible cards
Dialogue: 0,0:02:46.58,0:02:47.48,Default,,0000,0000,0000,,I could pick from.
Dialogue: 0,0:02:47.48,0:02:51.72,Default,,0000,0000,0000,,52 possible, equally likely\Nevents that we're dealing with.
Dialogue: 0,0:02:51.72,0:02:55.01,Default,,0000,0000,0000,,And how many of those\Nhave our hearts?
Dialogue: 0,0:02:55.01,0:02:57.77,Default,,0000,0000,0000,,Well, essentially 13\Nof them are hearts.
Dialogue: 0,0:02:57.77,0:03:00.18,Default,,0000,0000,0000,,For each of those suits\Nyou have 13 types.
Dialogue: 0,0:03:00.18,0:03:01.89,Default,,0000,0000,0000,,So there are 13\Nhearts in that deck.
Dialogue: 0,0:03:01.89,0:03:03.35,Default,,0000,0000,0000,,There are 13 diamonds\Nin that deck.
Dialogue: 0,0:03:03.35,0:03:04.97,Default,,0000,0000,0000,,There are 13 spades\Nin that deck.
Dialogue: 0,0:03:04.97,0:03:07.49,Default,,0000,0000,0000,,There are 13 clubs in that deck.
Dialogue: 0,0:03:07.49,0:03:12.57,Default,,0000,0000,0000,,So 13 of the 52 would result\Nin hearts, and both of these
Dialogue: 0,0:03:12.57,0:03:14.27,Default,,0000,0000,0000,,are divisible by 13.
Dialogue: 0,0:03:14.27,0:03:16.67,Default,,0000,0000,0000,,This is the same thing as 1/4.
Dialogue: 0,0:03:16.67,0:03:19.04,Default,,0000,0000,0000,,One in four times\NI will pick it out,
Dialogue: 0,0:03:19.04,0:03:21.69,Default,,0000,0000,0000,,or I have a one in four\Nprobability of getting a hearts
Dialogue: 0,0:03:21.69,0:03:24.62,Default,,0000,0000,0000,,when I randomly pick a card\Nfrom that shuffled deck.
Dialogue: 0,0:03:24.62,0:03:27.16,Default,,0000,0000,0000,,Now, let's do something that's\Na little bit more interesting,
Dialogue: 0,0:03:27.16,0:03:29.25,Default,,0000,0000,0000,,or maybe it's a little obvious.
Dialogue: 0,0:03:29.25,0:03:32.13,Default,,0000,0000,0000,,What's the probability\Nthat I pick something
Dialogue: 0,0:03:32.13,0:03:38.54,Default,,0000,0000,0000,,that is a Jack-- I'll just\Nwrite J-- and it is a hearts?
Dialogue: 0,0:03:42.12,0:03:44.23,Default,,0000,0000,0000,,Well, if you are reasonably\Nfamiliar with cards
Dialogue: 0,0:03:44.23,0:03:45.60,Default,,0000,0000,0000,,you'll know that\Nthere's actually
Dialogue: 0,0:03:45.60,0:03:47.90,Default,,0000,0000,0000,,only one card that is\Nboth a Jack and a heart.
Dialogue: 0,0:03:47.90,0:03:49.52,Default,,0000,0000,0000,,It is literally\Nthe Jack of hearts.
Dialogue: 0,0:03:49.52,0:03:50.53,Default,,0000,0000,0000,,So we're saying, what\Nis the probability
Dialogue: 0,0:03:50.53,0:03:52.87,Default,,0000,0000,0000,,that we pick the exact\Ncard, the Jack of hearts?
Dialogue: 0,0:03:52.87,0:03:56.20,Default,,0000,0000,0000,,Well, there's only\None event, one card,
Dialogue: 0,0:03:56.20,0:04:00.66,Default,,0000,0000,0000,,that meets this criteria\Nright over here,
Dialogue: 0,0:04:00.66,0:04:02.63,Default,,0000,0000,0000,,and there's 52 possible cards.
Dialogue: 0,0:04:02.63,0:04:04.63,Default,,0000,0000,0000,,So there's a one\Nin 52 chance that I
Dialogue: 0,0:04:04.63,0:04:07.65,Default,,0000,0000,0000,,pick the Jack of hearts--\Nsomething that is both a Jack
Dialogue: 0,0:04:07.65,0:04:09.71,Default,,0000,0000,0000,,and it's a heart.
Dialogue: 0,0:04:09.71,0:04:12.64,Default,,0000,0000,0000,,Now, let's do something a\Nlittle bit more interesting.
Dialogue: 0,0:04:12.64,0:04:14.43,Default,,0000,0000,0000,,What is the\Nprobability-- you might
Dialogue: 0,0:04:14.43,0:04:16.60,Default,,0000,0000,0000,,want to pause this and think\Nabout this a little bit
Dialogue: 0,0:04:16.60,0:04:17.81,Default,,0000,0000,0000,,before I give you the answer.
Dialogue: 0,0:04:17.81,0:04:20.02,Default,,0000,0000,0000,,What is the probability\Nof-- so I once again, I
Dialogue: 0,0:04:20.02,0:04:22.34,Default,,0000,0000,0000,,have a deck of 52\Ncards, I shuffled it,
Dialogue: 0,0:04:22.34,0:04:25.35,Default,,0000,0000,0000,,randomly pick a card from that\Ndeck-- what is the probability
Dialogue: 0,0:04:25.35,0:04:31.42,Default,,0000,0000,0000,,that that card that I pick from\Nthat deck is a Jack or a heart?
Dialogue: 0,0:04:31.42,0:04:33.05,Default,,0000,0000,0000,,So it could be the\NJack of hearts,
Dialogue: 0,0:04:33.05,0:04:35.41,Default,,0000,0000,0000,,or it could be the\NJack of diamonds,
Dialogue: 0,0:04:35.41,0:04:36.83,Default,,0000,0000,0000,,or it could be the\NJack of spades,
Dialogue: 0,0:04:36.83,0:04:38.45,Default,,0000,0000,0000,,or it could be the\NQueen of hearts,
Dialogue: 0,0:04:38.45,0:04:39.87,Default,,0000,0000,0000,,or it could be\Nthe two of hearts.
Dialogue: 0,0:04:39.87,0:04:41.33,Default,,0000,0000,0000,,So what is the\Nprobability of this?
Dialogue: 0,0:04:41.33,0:04:43.58,Default,,0000,0000,0000,,And this is a little bit\Nmore of an interesting thing,
Dialogue: 0,0:04:43.58,0:04:46.44,Default,,0000,0000,0000,,because we know, first\Nof all, that there
Dialogue: 0,0:04:46.44,0:04:49.91,Default,,0000,0000,0000,,are 52 possibilities.
Dialogue: 0,0:04:49.91,0:04:51.37,Default,,0000,0000,0000,,But how many of\Nthose possibilities
Dialogue: 0,0:04:51.37,0:04:57.01,Default,,0000,0000,0000,,meet these conditions that\Nit is a Jack or a heart.
Dialogue: 0,0:04:57.01,0:05:00.08,Default,,0000,0000,0000,,And to understand that,\NI'll draw a Venn diagram.
Dialogue: 0,0:05:00.08,0:05:02.65,Default,,0000,0000,0000,,Sounds kind of fancy,\Nbut nothing fancy here.
Dialogue: 0,0:05:02.65,0:05:04.74,Default,,0000,0000,0000,,So imagine that this\Nrectangle I'm drawing here
Dialogue: 0,0:05:04.74,0:05:06.82,Default,,0000,0000,0000,,represents all of the outcomes.
Dialogue: 0,0:05:06.82,0:05:09.77,Default,,0000,0000,0000,,So if you want, you could\Nimagine it has an area of 52.
Dialogue: 0,0:05:09.77,0:05:13.73,Default,,0000,0000,0000,,So this is 52 possible outcomes.
Dialogue: 0,0:05:13.73,0:05:16.73,Default,,0000,0000,0000,,Now, how many of those\Noutcomes result in a Jack?
Dialogue: 0,0:05:16.73,0:05:20.86,Default,,0000,0000,0000,,So we already learned, one out\Nof 13 of those outcomes result
Dialogue: 0,0:05:20.86,0:05:21.86,Default,,0000,0000,0000,,in a Jack.
Dialogue: 0,0:05:21.86,0:05:24.49,Default,,0000,0000,0000,,So I could draw a\Nlittle circle here,
Dialogue: 0,0:05:24.49,0:05:27.29,Default,,0000,0000,0000,,where that area-- and I'm\Napproximating-- represents
Dialogue: 0,0:05:27.29,0:05:28.52,Default,,0000,0000,0000,,the probability of a Jack.
Dialogue: 0,0:05:28.52,0:05:31.77,Default,,0000,0000,0000,,So it should be\Nroughly 1/13, or 4/52,
Dialogue: 0,0:05:31.77,0:05:33.46,Default,,0000,0000,0000,,of this area right over here.
Dialogue: 0,0:05:33.46,0:05:36.06,Default,,0000,0000,0000,,So I'll just draw it like this.
Dialogue: 0,0:05:36.06,0:05:38.50,Default,,0000,0000,0000,,So this right over here is\Nthe probability of a Jack.
Dialogue: 0,0:05:44.31,0:05:46.66,Default,,0000,0000,0000,,There's four possible\Ncards out of the 52.
Dialogue: 0,0:05:46.66,0:05:51.56,Default,,0000,0000,0000,,So that is 4/52,\Nor one out of 13.
Dialogue: 0,0:05:54.27,0:05:56.47,Default,,0000,0000,0000,,Now, what's the probability\Nof getting a hearts?
Dialogue: 0,0:05:56.47,0:05:58.54,Default,,0000,0000,0000,,Well, I'll draw another\Nlittle circle here
Dialogue: 0,0:05:58.54,0:05:59.53,Default,,0000,0000,0000,,that represents that.
Dialogue: 0,0:05:59.53,0:06:03.54,Default,,0000,0000,0000,,13 out of 52 cards\Nrepresent a heart.
Dialogue: 0,0:06:03.54,0:06:05.88,Default,,0000,0000,0000,,And actually, one of those\Nrepresents both a heart
Dialogue: 0,0:06:05.88,0:06:06.92,Default,,0000,0000,0000,,and a Jack.
Dialogue: 0,0:06:06.92,0:06:09.06,Default,,0000,0000,0000,,So I'm actually going\Nto overlap them,
Dialogue: 0,0:06:09.06,0:06:12.87,Default,,0000,0000,0000,,and hopefully this will\Nmake sense in a second.
Dialogue: 0,0:06:12.87,0:06:18.01,Default,,0000,0000,0000,,So there's actually 13\Ncards that are a heart.
Dialogue: 0,0:06:18.01,0:06:19.53,Default,,0000,0000,0000,,So this is the number of hearts.
Dialogue: 0,0:06:22.18,0:06:25.11,Default,,0000,0000,0000,,And actually, let me write this\Ntop thing that way as well.
Dialogue: 0,0:06:25.11,0:06:27.38,Default,,0000,0000,0000,,It makes it a little bit\Nclearer that we're actually
Dialogue: 0,0:06:27.38,0:06:32.32,Default,,0000,0000,0000,,looking at the number of Jacks.
Dialogue: 0,0:06:37.39,0:06:39.21,Default,,0000,0000,0000,,And of course,\Nthis overlap right
Dialogue: 0,0:06:39.21,0:06:42.92,Default,,0000,0000,0000,,here is the number of Jacks\Nand hearts-- the number
Dialogue: 0,0:06:42.92,0:06:45.47,Default,,0000,0000,0000,,of items out of this 52 that\Nare both a Jack and a heart--
Dialogue: 0,0:06:45.47,0:06:47.16,Default,,0000,0000,0000,,it is in both sets here.
Dialogue: 0,0:06:47.16,0:06:50.81,Default,,0000,0000,0000,,It is in this green circle and\Nit is in this orange circle.
Dialogue: 0,0:06:50.81,0:06:53.50,Default,,0000,0000,0000,,So this right over here--\Nlet me do that in yellow
Dialogue: 0,0:06:53.50,0:06:56.60,Default,,0000,0000,0000,,since I did that problem in\Nyellow-- this right over here
Dialogue: 0,0:06:56.60,0:06:58.21,Default,,0000,0000,0000,,is a number of Jacks and hearts.
Dialogue: 0,0:06:58.21,0:06:59.71,Default,,0000,0000,0000,,So let me draw a\Nlittle arrow there.
Dialogue: 0,0:06:59.71,0:07:01.59,Default,,0000,0000,0000,,It's getting a little\Ncluttered, maybe
Dialogue: 0,0:07:01.59,0:07:03.32,Default,,0000,0000,0000,,I should draw a little\Nbit bigger number.
Dialogue: 0,0:07:11.04,0:07:12.96,Default,,0000,0000,0000,,And that's an\Noverlap over there.
Dialogue: 0,0:07:12.96,0:07:15.67,Default,,0000,0000,0000,,So what is the probability\Nof getting a Jack or a heart?
Dialogue: 0,0:07:15.67,0:07:18.45,Default,,0000,0000,0000,,So if you think about\Nit, the probability
Dialogue: 0,0:07:18.45,0:07:20.26,Default,,0000,0000,0000,,is going to be the\Nnumber of events
Dialogue: 0,0:07:20.26,0:07:22.98,Default,,0000,0000,0000,,that meet these conditions,\Nover the total number events.
Dialogue: 0,0:07:22.98,0:07:25.06,Default,,0000,0000,0000,,We already know the total\Nnumber of events are 52.
Dialogue: 0,0:07:25.06,0:07:27.04,Default,,0000,0000,0000,,But how many meet\Nthese conditions?
Dialogue: 0,0:07:27.04,0:07:29.95,Default,,0000,0000,0000,,So it's going to be the\Nnumber-- you could say,
Dialogue: 0,0:07:29.95,0:07:32.11,Default,,0000,0000,0000,,well, look at the green\Ncircle right there says
Dialogue: 0,0:07:32.11,0:07:35.58,Default,,0000,0000,0000,,the number that gives us a Jack,\Nand the orange circle tells us
Dialogue: 0,0:07:35.58,0:07:37.58,Default,,0000,0000,0000,,the number that\Ngives us a heart.
Dialogue: 0,0:07:37.58,0:07:41.10,Default,,0000,0000,0000,,So you might want to say,\Nwell, why don't we add up
Dialogue: 0,0:07:41.10,0:07:43.80,Default,,0000,0000,0000,,the green and the\Norange, but if you
Dialogue: 0,0:07:43.80,0:07:46.05,Default,,0000,0000,0000,,did that, you would\Nbe double counting,
Dialogue: 0,0:07:46.05,0:07:47.63,Default,,0000,0000,0000,,Because if you add\Nit up-- if you just
Dialogue: 0,0:07:47.63,0:07:52.58,Default,,0000,0000,0000,,did four plus 13--\Nwhat are we saying?
Dialogue: 0,0:07:52.58,0:07:55.98,Default,,0000,0000,0000,,We're saying that\Nthere are four Jacks
Dialogue: 0,0:07:55.98,0:08:00.17,Default,,0000,0000,0000,,and we're saying that\Nthere are 13 hearts.
Dialogue: 0,0:08:00.17,0:08:04.23,Default,,0000,0000,0000,,But in both of these, when we\Ndo it this way, in both cases
Dialogue: 0,0:08:04.23,0:08:06.24,Default,,0000,0000,0000,,we are counting\Nthe Jack of hearts.
Dialogue: 0,0:08:06.24,0:08:07.78,Default,,0000,0000,0000,,We're putting the\NJack of hearts here
Dialogue: 0,0:08:07.78,0:08:09.37,Default,,0000,0000,0000,,and we're putting the\NJack of hearts here.
Dialogue: 0,0:08:09.37,0:08:10.87,Default,,0000,0000,0000,,So we're counting\Nthe Jack of hearts
Dialogue: 0,0:08:10.87,0:08:13.89,Default,,0000,0000,0000,,twice, even though there's\Nonly one card there.
Dialogue: 0,0:08:13.89,0:08:17.09,Default,,0000,0000,0000,,So you would have to subtract\Nout where they're common.
Dialogue: 0,0:08:17.09,0:08:21.09,Default,,0000,0000,0000,,You would have to\Nsubtract out the item that
Dialogue: 0,0:08:21.09,0:08:23.39,Default,,0000,0000,0000,,is both a Jack and a heart.
Dialogue: 0,0:08:23.39,0:08:24.99,Default,,0000,0000,0000,,So you would subtract out a 1.
Dialogue: 0,0:08:24.99,0:08:26.80,Default,,0000,0000,0000,,Another way to\Nthink about it is,
Dialogue: 0,0:08:26.80,0:08:29.13,Default,,0000,0000,0000,,you really want to figure\Nout the total area here.
Dialogue: 0,0:08:33.92,0:08:36.59,Default,,0000,0000,0000,,And let me zoom in-- and I'll\Ngeneralize it a little bit.
Dialogue: 0,0:08:36.59,0:08:38.09,Default,,0000,0000,0000,,So if you have one\Ncircle like that,
Dialogue: 0,0:08:38.09,0:08:41.03,Default,,0000,0000,0000,,and then you have another\Noverlapping circle like that,
Dialogue: 0,0:08:41.03,0:08:43.73,Default,,0000,0000,0000,,and you wanted to figure\Nout the total area of both
Dialogue: 0,0:08:43.73,0:08:45.70,Default,,0000,0000,0000,,of these circles\Ncombined, you would
Dialogue: 0,0:08:45.70,0:08:47.26,Default,,0000,0000,0000,,look at the area of this circle.
Dialogue: 0,0:08:50.34,0:08:53.73,Default,,0000,0000,0000,,And then you could add it\Nto the area of this circle.
Dialogue: 0,0:08:53.73,0:08:56.53,Default,,0000,0000,0000,,But when you do that, you'll\Nsee that when you add the two
Dialogue: 0,0:08:56.53,0:08:59.27,Default,,0000,0000,0000,,areas, you're counting\Nthis area twice.
Dialogue: 0,0:08:59.27,0:09:01.27,Default,,0000,0000,0000,,So in order to only\Ncount that area once,
Dialogue: 0,0:09:01.27,0:09:04.51,Default,,0000,0000,0000,,you have to subtract\Nthat area from the sum.
Dialogue: 0,0:09:04.51,0:09:10.20,Default,,0000,0000,0000,,So if this area has\NA, this area is B,
Dialogue: 0,0:09:10.20,0:09:15.83,Default,,0000,0000,0000,,and the intersection\Nwhere they overlap is C,
Dialogue: 0,0:09:15.83,0:09:20.37,Default,,0000,0000,0000,,the combined area is\Ngoing to be A plus B-- --
Dialogue: 0,0:09:20.37,0:09:23.49,Default,,0000,0000,0000,,minus where they\Noverlap-- minus C.
Dialogue: 0,0:09:23.49,0:09:24.95,Default,,0000,0000,0000,,So that's the same\Nthing over here,
Dialogue: 0,0:09:24.95,0:09:26.87,Default,,0000,0000,0000,,we're counting all\Nthe Jacks, and that
Dialogue: 0,0:09:26.87,0:09:28.04,Default,,0000,0000,0000,,includes the Jack of hearts.
Dialogue: 0,0:09:28.04,0:09:29.66,Default,,0000,0000,0000,,We're counting all\Nthe hearts, and that
Dialogue: 0,0:09:29.66,0:09:31.23,Default,,0000,0000,0000,,includes the Jack of hearts.
Dialogue: 0,0:09:31.23,0:09:33.25,Default,,0000,0000,0000,,So we counted the\NJack of hearts twice,
Dialogue: 0,0:09:33.25,0:09:35.26,Default,,0000,0000,0000,,so we have to subtract\N1 out of that.
Dialogue: 0,0:09:35.26,0:09:37.64,Default,,0000,0000,0000,,This is going to be\N4 plus 13 minus 1,
Dialogue: 0,0:09:37.64,0:09:40.28,Default,,0000,0000,0000,,or this is going to be 16/52.
Dialogue: 0,0:09:42.85,0:09:48.25,Default,,0000,0000,0000,,And both of these things\Nare divisible by 4.
Dialogue: 0,0:09:48.25,0:09:51.89,Default,,0000,0000,0000,,So this is going to be the\Nsame thing as, divide 16 by 4,
Dialogue: 0,0:09:51.89,0:09:52.67,Default,,0000,0000,0000,,you get 4.
Dialogue: 0,0:09:52.67,0:09:55.33,Default,,0000,0000,0000,,52 divided by 4 is 13.
Dialogue: 0,0:09:55.33,0:10:01.46,Default,,0000,0000,0000,,So there's a 4/13 chance that\Nyou'd get a Jack or a hearts.