What is the conditional probability that a randomly selected family owns a dog diven that it doesn't own a cat?

The question has some details missing, here is the complete question;

In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 29% of all the families own a cat. What is the probability that a randomly selected family owns a dog? What is the conditional probability that a randomly selected family owns a dog diven that it doesn't own a cat?

Step-by-step explanation:

P (Dog) = P (D) = 0.30

P (C|D) = 0.20

P (C) = 0.29

P (C') = 1 - 0.29 = 0.71

What is the conditional probability that a randomly selected family owns a dog diven that it doesn't own a cat?

First calculate P (dog and no cat) = P (D) - P (DnC) = 0.29 - (0.30 x 0.20)

= 0.23

P (dog|no cat) = P (dog no cat) / P (no cat)

= 0.23 x 0.71 = 0.1633