In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is (a) the probability that a randomly selected family owns both a dog and a cat?

0.0792

Step-by-step explanation:

the probability that a family owns a dog = P (D) = 36%=0.36

the probability that a family owns a dog also owns a cat=P (CnD) = 22%=0.22

the probability that a family owns a cat = P (C) = 30%=0.3

therefore, Probability that a randomly selected family owns both a dog and cat is given as

P (C∪D) = P (C∩D) * P (D)

=0.22*0.36

=0.0792

≈0.08