Original subtitles

Instructor: Hello folks, in this video

we are going to focus on visual aids and graphs

to help you better understand sets and events.

Take events A and B for example,

we express the set of values that satisfy each

of them as circles, one for A and another one for B.

Any element that is part of either set will be represented

by a point in the appropriate circle.

Since we can have additional events

the more events we have, the more circles we draw.

Let's only focus on A and B for now.

The two circles can either not touch at all, intersect,

or one can completely overlap the other.

We are going to explore each of these scenarios

in more detail, right now.

If the two circles never touch

then the two events can never happen simultaneously.

Essentially, event A occurring guarantees

that event B is not occurring and vice versa.

Continuing with another card example, getting a diamond

and getting a heart would be such a situation.

If we get a heart, we can't get a diamond

and if we get a diamond, we can't get a heart

since each card has exactly one suit

that's the easiest scenario and is the one

we assumed so far in the course.

In this section though, we will focus on the other two,

when they are intersecting,

or when one is a subset of the other.

Now, if these circles intersect, it means

that the two events can occur at the same time.

Imagine we draw a card from a standard deck

of playing cards, event A is drawing a diamond

and event B is drawing a queen.

The area where they intersect

will be represented solely by the queen of diamonds.

The remaining area of A will represent all other diamonds

whereas the area of B outside of that

will represent all other queens.

So these circles seem quite useful, don't they?

Let's explore the last scenario.

The third case happens if one circle completely

overlaps another, that means that one event

can only ever occur if the other one does as well.

For instance, event A could be drawing a red card

and event B could be drawing a diamond.

The circle of B is completely contained inside A

so we can only ever get a diamond if we get a red card.

Notice that if the card we drew is black

it cannot be a diamond thus, if event A does not occur,

then neither does event B.

However, because we can draw a heart

it is possible to get a red card that isn't a diamond.

Therefore, event B not occurring

does guarantee event A not occurring.

In short, if an outcome is not part of a set

it cannot be part of any of its subsets.

However, an outcome not being part of some subset

does not exclude it from the entirety of the greater set.

Okay, that pretty much summarizes the relationships

that the sets of two events can have.

Of course, we can have three, four,

or as many events as we want and the relationships

between each two will always be represented

by one of the three ways we just went over.

In the next two lectures we are going

to introduce intersections and unions.

We will frequently use these definitions going forward.

Thanks for watching.