00:01
In a class of 50 students appearing for an examination of singapore national university, 20 failed in accounting, 21 failed in mathematics, and 27 failed in cost accounting.
00:16
10 failed in accounting and cost accounting, 13 failed in both mathematics and cost accounting, and 7 failed in all three subjects.
00:23
We want to start with the all three subjects number.
00:27
So 7 is going to go right here in this space where all three of those, those circles intersect.
00:34
Now from that, let's work backwards.
00:38
So they told us that 13 failed both in mathematics and cost accounting.
00:44
We've already used seven in that group there.
00:48
So we'll need to take 13 minus seven.
00:50
So that means six will go into this space here.
00:54
10 failed in accounting and cost accounting.
00:57
We've used seven of those.
00:58
So three is going to go in this space here.
01:02
Then we are told that 27 failed in costa county.
01:05
We've already used 16, so that leaves 11.
01:11
And we don't have a value for this space here.
01:15
We're not told how many failed both accounting and mathematics, but we are told that 20 failed accounting.
01:22
We've already used 10.
01:24
So i'm going to put this value here in a different color, kind of with an asterisk notation form.
01:32
Myself to say, okay, i don't know necessarily that they were all just accounting.
01:37
Some of them could have been accounting in math.
01:40
And then i'll do the same thing for math because i'm told that 21 failed in mathematics.
01:46
We already use 13, which leaves 8.
01:50
That would be dispersed among the circle and the shared part with accounting.
01:59
So the first task was to create this venn diagram.
02:03
There's one more piece of data that we should put in there.
02:06
We've used up of our 50, we used up 45, which means there are five that are not part of that interlocking circle.
02:14
For part two, find the numbers of failures in accounting only.
02:20
At this point, with the information we're given, we're going to have to assume that this 10 is accounting only and that there were no students that failed both accounting and math.
02:32
And so without further information, that's what we're kind of stuck with there.
02:39
And for part three, find how many students passed all three subjects.
02:45
So these circles are students who failed one, two, or three classes.
02:50
This group out here that's outside of the circle, again, we used up 45 of our 50, so there are five that didn't fail anything.
03:01
Now we're going to move on to a different concept.
03:04
So i'm going to go ahead and slide this over and make it a little bit smaller.
03:09
So for part b, given that u, our universal set, is 0 ,1, dot, dot, dot, until 9, and that a is the set 2, 4, 6, b is the set 1, 3, 5, and 7, and c is the set 6 and 7.
03:41
We're going to answer a bunch of different probability statements...