Question

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.

Answer 1

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:

`bar(bar(Omega))=5,000` it is the total number of people asked

`bar(bar(A))=3,500` it is the number of people who are in favour of gun central laws

`bar(bar(A^'))=5,000-3,500=1,500`

Now we can calculate the probabilities:

`P(A)=3500/5000=7/10`

`P(A^')=1500/5000=3/10`