Question

in the U.S, 37% of households have dogs, 30% of households have cats, and 7% of households have both cats and dogs. what percentage of households have a cat or a dog?

Step 1

**Addition rule of probability:**

Addition rule of probability indicates the happening either of the events that are involved.

Consider two events *A* and *B*, the happening of either of the events *A* or *B* is obtained as follows:

Step 2

**Obtain the probability that the households have either a cat or a dog.**

Denote the event “a household have dogs” as *A.*

It is given that, 37% of households have dogs.

That is, the probability that a household have a dog is *P*(*A*) = 0.37.

Denote the event “a household have cats” as *B.*

It is given that, 30% of households have cats.

That is, the probability that a household have cats is *P*(*B*) = 0.3.

It is given that, 7% of households have both dogs and cats.

That is, the probability that a household have a dog or a cat is *P*(*A* ∪*B*) = 0.07.

The probability that the households have either a cat or a dog is obtained as 0.6 from the calculation given below:

Step 3

**Obtain the percentage of households that have a cat or a dog.**

The probability that the households have either a cat or a dog is 0.6.

The perce...

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