(1 point) In a certain community, 40% of the families own a dog, and 20% of...

(1 point) In a certain community, 40% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 36% 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 doesn't own a dog given that it owns a cat?

Solutions

Expert Solution

In a certain community, it is known that 40% of the families own a dog, and 20% of the families that own a dog also own a cat.

It is also known that 36% of all families own a cat.

Let,

D= event that a family owns a dog

C=event that a family owns a cat.

Now, it is given,

Question a

What is the probability that a randomly selected family owns a dog ?

The answer is

Question b

What is the probability that a randomly selected family does not own a dog, given it owns a cat.

To find

By definition of conditional probability, this is

So, the probability that a family does not own a dog, given it owns a cat, is 0.77.

orchestra answered 1 year ago

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