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

1 Answer
Daniel L.
Jan 30, 2017

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}

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