Question

Use the survey results to find the probability that a respondent has a​ pet, given that the respondent has had a pet.

37​% have a pet now and have had a pet.

63​% do not have a pet now.

81​% have had a pet.

19​% do not have a pet now and have never had a pet.

The Probability that the respondent has a pet given that the respondent has had a pet is ?

Show your work

Answer 1

Probability that the respondent has a pet given that the respondent has had a pet is
`(37)/(81)` or 0.46.

Explanation:

We are given the following results below;

37​% have a pet now and have had a pet.

63​% do not have a pet now.

81​% have had a pet.

19​% do not have a pet now and have never had a pet.

Let event B = respondent has a pet now

Now, Probability that the respondent has had a pet = P(A) = 0.81

Probability that the respondent has a pet now and has had a pet =
`P(A \bigcap B)` = 0.37

So, Probability that the respondent has a pet given that the respondent has had a pet is given by = P(B/A)

This conditional probability is solved as ;

P(B/A) =
`(P(A \bigcap B))/(P(A))`

=
`(0.37)/(0.81)` = 0.46.