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

Answer:

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