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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?

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?

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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:

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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(AB) = 0.07.

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

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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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