One household is to be selected at random from a town. the probability that the household has a cat is 0.20.2 . the probability that the household has a dog is 0.40.4 . the probability that the household has a cat or a dog is 0.50.5 . what is the probability that the household has a dog, given that the household has a cat? show your work on the scratchpad.

There is a 50% probability that the household has a dog, given that the household has a cat.

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a household has a cat.

B is the probability that a household has a dog.

We have that:

In which a is the probability that a household has a cat but not a dog and is the probability that a household has both a cat and a dog.

By the same logic, we have that:

The probability that the household has a cat or a dog is 0.5

The probability that the household has a dog is 0.4

The probability that the household has a cat is 0.2.

So

What is the probability that the household has a dog, given that the household has a cat?

20% of the households have a cat, and 10% have both a cat and a dog. So

There is a 50% probability that the household has a dog, given that the household has a cat.

the answer to this question is in the pic

0 is its x and y coordinate