Question

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

Answer 1

Answer:

Probability that the respondent has a pet given that the respondent has had a pet is  $\frac{37}{81}$  or 0.46.

Step-by-step 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)  =  $\frac{P(A \bigcap B)}{P(A)}$

                 =  $\frac{0.37}{0.81}$  = 0.46.