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

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