1
00:00:00,800 --> 00:00:06,660
The coin and dice examples in the previous video are all examples of mutually exclusive events.

2
00:00:06,980 --> 00:00:11,230
This just means that only a single event can occur at the same time.

3
00:00:13,420 --> 00:00:20,380
So if we have a look at the single coin toss event example, we have a set of events of a heads or tails

4
00:00:20,380 --> 00:00:26,890
being shown on the up face so we can even get a heads or tails is impossible for us to flip a coin and

5
00:00:26,890 --> 00:00:28,900
get a heads and tails at the same time.

6
00:00:29,290 --> 00:00:33,040
So the event, heads and tails are mutually exclusive.

7
00:00:34,210 --> 00:00:39,190
If we also have a look at the single roll example, we can have a set of the possible events being the

8
00:00:39,190 --> 00:00:45,700
one, two, three, four, five or six dots showing up or down here, but is impossible to roll the

9
00:00:45,700 --> 00:00:49,300
dice with multiple faces shown on the up face.

10
00:00:49,300 --> 00:00:54,190
At the same time, it is impossible to roll a three and a four at the same time.

11
00:00:54,910 --> 00:00:58,810
Only a single one of each of these events occur at a single time.

12
00:01:00,690 --> 00:01:07,350
So this can be expressed mathematically, so given a set of possible events, A and B. So the set of

13
00:01:07,350 --> 00:01:15,720
events and B basic probability says the probability of getting an A or A B or so any of the complete

14
00:01:15,720 --> 00:01:19,430
set is just the sum of the probabilities and it has to equal one.

15
00:01:19,740 --> 00:01:22,800
We have to get one event out of the total set.

16
00:01:24,440 --> 00:01:31,460
Now, events A and B occurring simultaneously is impossible, so the probability of getting A and B

17
00:01:31,820 --> 00:01:39,290
equals zero, then events A and B are mutually exclusive is impossible to get an event A and B occurring

18
00:01:39,290 --> 00:01:40,190
at the same time.

19
00:01:43,280 --> 00:01:46,040
But events do not have to be mutually exclusive.

20
00:01:46,670 --> 00:01:49,940
It is possible to get different events occurring at the same time.

21
00:01:50,390 --> 00:01:53,480
So here we have a static pack of playing cards.

22
00:01:53,900 --> 00:01:59,950
So we have numbers from Ace all the way up to King, and we have four different suits.

23
00:02:01,100 --> 00:02:07,770
Now, it is possible to pull out a hot card from this example, from this deck.

24
00:02:08,600 --> 00:02:11,900
It is also possible to pull out a king from this deck.

25
00:02:12,780 --> 00:02:18,930
And it's also possible to pull out a king of hearts, so the probability of pulling out a king and a

26
00:02:18,930 --> 00:02:20,620
heart does not equal zero.

27
00:02:21,060 --> 00:02:23,980
So this is a non mutually exclusive event.

28
00:02:23,980 --> 00:02:29,310
In the event of pulling out a heart and pulling out a king is not mutually exclusive.

29
00:02:32,440 --> 00:02:38,320
So let's have a look in a bit more mathematical detail, so, for example, if we wanted to work out

30
00:02:38,320 --> 00:02:44,170
the probability of pulling out a hot card, we can see that there are 13 hot cards in the stick and

31
00:02:44,170 --> 00:02:46,510
the deck is made up of 52 cards.

32
00:02:46,850 --> 00:02:51,870
Therefore, the probability of pulling out a hot card is just 13, over 52.

33
00:02:52,480 --> 00:02:54,610
And we can do the same thing for the king cards.

34
00:02:55,060 --> 00:02:59,440
So we can easily see there are four cards and there's 52 cards in the deck.

35
00:02:59,440 --> 00:03:03,080
So the probability of pulling out a king is for over 52.

36
00:03:04,540 --> 00:03:10,100
So now say we want to work out the probability of pulling out a card or a king card.

37
00:03:10,600 --> 00:03:16,270
Now, when, Wolf, we're looking at the mutually exclusive events, we could just add the two probabilities

38
00:03:16,270 --> 00:03:21,760
together so we could do the probability of a heart or the probability of the king and the probabilities

39
00:03:21,760 --> 00:03:22,290
together.

40
00:03:22,960 --> 00:03:27,360
So we could be doing this for non mutually exclusive events.

41
00:03:27,490 --> 00:03:33,910
This is not a valid and we can easily see from this sort of Venn diagram up here, we can see that this

42
00:03:34,420 --> 00:03:37,900
set of events and this set of events intersect each other.

43
00:03:37,900 --> 00:03:42,260
So they have a common event that can occur at the same time.

44
00:03:42,460 --> 00:03:48,040
So if we add this probability up and this probability up together, we can see that we've included this

45
00:03:48,040 --> 00:03:52,120
probability of the king of hearts happening live, included it twice.

46
00:03:53,140 --> 00:03:55,300
So this is not going to give us the correct probability.

47
00:03:56,050 --> 00:04:02,590
So the correct way to calculate the probability of pulling out a heart or a king is going to be the

48
00:04:02,680 --> 00:04:07,420
sum of the probabilities of the heart and king minus the common intersection, which is going to be

49
00:04:07,420 --> 00:04:13,210
the probability of pulling out of king and heart at the same time so we can put numbers under this.

50
00:04:13,780 --> 00:04:19,300
So we have probability of pulling out of King is the four and a 50 to the probability of pulling out

51
00:04:19,300 --> 00:04:27,010
a heart is 13 of 52 and the probability of pulling out of king and a heart at the same time or simply

52
00:04:27,010 --> 00:04:28,500
say that's only a single event.

53
00:04:28,510 --> 00:04:30,150
So that's just one over 52.

54
00:04:31,030 --> 00:04:34,630
So if we evaluate this equation, we get 16, 52.

55
00:04:34,630 --> 00:04:37,780
So that's a probability of pulling out a heart or a king.

56
00:04:38,110 --> 00:04:46,120
And we can quickly verify this because we can see there's 13 cards here and then we have 14, 15, 16.

57
00:04:46,510 --> 00:04:51,990
So there's 16 out of 52 ways of pulling out a king or a heart card.

58
00:04:53,980 --> 00:04:59,350
So to summarize what we've talked about in this video, mutually exclusive events means that the probability

59
00:04:59,350 --> 00:05:03,440
of Event A and Event B occurring at the same time is zero.

60
00:05:03,670 --> 00:05:07,660
So if the probability is zero, then the events are mutually exclusive.

61
00:05:08,260 --> 00:05:12,600
If the probability is not zero, then the events are not mutually exclusive.

62
00:05:12,610 --> 00:05:16,720
It is possible for Event A and Event B to occur at the same time.

63
00:05:17,870 --> 00:05:23,000
Now, the probability of non mutually exclusive events can be written in this equation down here, so

64
00:05:23,000 --> 00:05:28,460
the probability of A or the probability a B is just the sum of the probability of the individual event,

65
00:05:28,790 --> 00:05:31,840
minus the probability of A and B occurring.

66
00:05:32,660 --> 00:05:38,600
So we could quickly see that if the events are mutually exclusive, then this is just going to be this

67
00:05:38,730 --> 00:05:40,430
part just going to be equal to zero.

68
00:05:40,760 --> 00:05:46,730
And we're going to be left with our original equation as a probability of A and A probability, B or

69
00:05:46,730 --> 00:05:52,490
B, but if they're not mutually exclusive, then we have to take that into account by subtracting a

70
00:05:52,490 --> 00:05:58,190
single common the by subtracting the common overlap between the events.