Original subtitles

Tutor: Welcome back.

Toward the end of the last section,

we mentioned mutually exclusive sets without explaining

what they are in detail.

Well, mutually exclusive sets are sets which are not allowed

to have any overlapping elements,

graphically their circles never intersect.

During the last couple of lectures,

we introduced some important characteristics of such events.

Mutually exclusive sets have the empty set

as their intersection.

Therefore, if the intersection of any number

of sets is the empty set,

then they must be mutually exclusive and vice versa.

What about their union?

If some sets are mutually exclusive,

their union is simply the sum

of all separate individual sets.

Okay, earlier in the course we also mentioned

how events have complements.

In a similar way, sets have complements too.

Such compliments consist of all values

that are parts of the sample space,

but not part of the set.

For instance, imagine a set consisting

of all the odd numbers, its complement would be the set

of all even numbers.

One thing to remember about complements

is that they are always mutually exclusive,

however not all mutually exclusive sets are complements.

For instance, imagine A is the set of all even numbers

and B is the set of all numbers ending in five.

We know that any number ending with five is odd,

so these two sets are definitely mutually exclusive.

However, the complement of all even is all odd

and not just the ones ending with five.

Therefore, a number like 13 would be part of the compliment,

but not the set B.

After the short clarification

we are ready to dive deeper into probability theory.

In the next lecture, we are going to explain

the differences between independent and dependent events.

Thanks for watching.