Question

What is a simple event in probability? What is a complementary event?

Answer 1

See explanation.

Explanation:

A elementary event is (exactly speaking) a primary oobject which is not defined (as for example a point or a number).

More generally it is a "basic result" of a probability experiment. For example if a die is thrown the possible results (i.e. elementary events) are `1,2,3,4,5` and `6`

A set of all elementary events is called a sample space and denoted by `Omega`

An event is any subset of `Omega`

A complementary event of `A` is a set:

`A'={omega in Omega:omega !in A}`

so the complementary event consists of all elementary events which are not in the event `A`

Example

I wrote earlier about an experiment of a die throw. Its sample space is (as I wrote) a set of numbers `1`-`6`

`Omega = {1,2,3,4,5,6}`

Let `A` be an event a prime number is thrown.

Then `A={2,3,5}`, because in the set `Omega` only `2,3` and `5` are prime numbers

A complementary event would be `A'` - a number which is not prime is thrown, so

`A'={1,4,6}`