Mathematics: 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

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Pet ownership suppose that 25% of people have a

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paiged55

14.03.2022

Mathematics

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.

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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

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