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

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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.

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.

##### 1 Answer

See explanation.

#### Explanation:

The complementary event of **not** in

#A^'=Omega-A#

In the given example we have:

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

*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:

Now we can calculate the probabilities: