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 …

Question

asked Feb 21, 2021 230k views

1 Answer

Martin Gross · Answer 1 · 2021-02-25T21:36:38+0000

Answer:

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.