# What is the complementary event of A?What are the probabilities of A and its complement?

## In a group of 5000 adults,3500 are in favour of gun central laws,1200 are against such laws and 300 have no opinion.One adult is randomly selected from this group.Let A be the event that this adult is in favour of gun central laws.

May 17, 2018

See explanation.

#### Explanation:

The complementary event of $A$ is the whole set of elemntary events which are not in $A$:

## ${A}^{'} = \Omega - A$

In the given example we have:

The event $A$ is the chosen person is in favour of gun central laws, so the complementary event is:

${A}^{'}$ - the chosen person did not answer, that he/she is in favour of gun central laws.

This means that the person either answered NO, or said that he/she does not have an opinion on the case.

To calculate the probabilities we have to write down the data first:

$\overline{\overline{\Omega}} = 5 , 000$ it is the total number of people asked

$\overline{\overline{A}} = 3 , 500$ it is the number of people who are in favour of gun central laws

$\overline{\overline{{A}^{'}}} = 5 , 000 - 3 , 500 = 1 , 500$

Now we can calculate the probabilities: