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

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

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Maria 1 week 2022-01-12T16:14:31+00:00 1 Answer 0 views 0

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    2022-01-12T16:15:41+00:00

    Answer:

    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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