Question

Pet ownership suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both. what is the probability that someone owns a dog or a cat

Answer 1

25+29-12=42
42% own either a dog, a cat, or both
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Answer 2

There is a 42% probability that someone owns a dog or a cat.

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 person has a dog.

B is the probability that a person has a cat.

We have that:

`A = a + (A \cap B)`

In which a is the probability that a person has a dog but not a cat and
`A \cap B` is the probability that a person has both a dog and a cat.

By the same logic, we have that:

`B = b + (A \cap B)`

We start finding the values from the intersection of these sets:

12% of people own both.

This means that
`A \cap B = 0.12`

29% of people have a cat.

This means that
`B = 0.29`. So:

`B = b + (A \cap B)`

`0.29 = b + 0.12`

`b = 0.17`

25% of people have a dog

This means that
`A = 0.25`. So:

`A = a + (A \cap B)`

`0.25 = a + 0.12`

`a = 0.13`

What is the probability that someone owns a dog or a cat?

`P = a + b + (A \cap B)`.

`P = 0.13 + 0.17 + 0.12 = 0.42`

There is a 42% probability that someone owns a dog or a cat.