00:01
We have a probability table.
00:02
We need to complete it and then find some certain probabilities.
00:06
So we have five possible outcomes.
00:09
A, b, c, d and e.
00:13
And we have most of this information.
00:16
We have 0 .3, 0 .02, 0 .5 and 0 .08.
00:21
First thing we need to do, what's the probability of outcome e? so the key to a probability distribution table is that the sum of the probabilities, so the probabilities of, let's call them xi for each outcome, if you add them up, you get a total of 1.
00:41
So if i add all of these up, i have 0 .1, 0 .6, okay, 0 .9, which means e has to be 0 .1.
00:52
Now they all add up to a total of 1, and we can proceed with the question.
00:59
So the first part is the probability of a, c or e.
01:11
So any of these meet the criteria.
01:14
All we need to do is add up these possible outcomes.
01:19
So 0 .3 plus 0 .5 plus 0 .1.
01:25
It gives us a total of 0 .9.
01:29
So there's a 30 % chance that a will happen, a 50 % chance for c will happen, a 10 % chance for e will happen.
01:36
The probability of one of these three things happening is 90%.
01:40
0 .9.
01:43
For part b, we need e, union, f.
01:52
This symbol here is union.
01:55
It means you can have e or f or both.
01:58
Anything that falls into one or both of these categories meets the criteria there.
02:03
So if we have a look, e is a, c or e.
02:08
So all of those have to be included.
02:10
So there's a, there's c, there's c, c and there's e.
02:15
F contains b, c and e.
02:19
So we'll add in b.
02:20
We don't want to count c or e twice, so since those are already counted, well, libos, and that gives us 0 .92...