Question

A survey found that 39% of the population owned dogs, 22% owned
cats, and 8% of the population owned both a cat and a dog? Find
the probability that a person owns a cat or a dog.

Answer 1

Answer:

53% probability that a person owns a cat or a dog.

Step-by-step explanation:

I am going to solve this question building the Venn's diagram of these probabilities,

We have that:

P(A) is the probability that a person owns a dog.

P(B) is the probability that a person owns a cat.

8% of the population owned both a cat and a dog

This means that $P(A \cap B) = 0.08$

22% owned cats

This means that $P(B) = 0.22$

39% of the population owned dogs

This means that $P(A) = 0.39$

Find the probability that a person owns a cat or a dog.

This is $P(A \cup B)$, which is given by:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

So

$P(A \cup B) = 0.39 + 0.22 - 0.08 = 0.53$

53% probability that a person owns a cat or a dog.

Answer 2

Answer:

0.53

Step-by-step explanation:

Percentage who owned dogs, n(D)=39%

Percentage who owned cats, n(C)=22%

Percentage who owned both dogs and cats, $n(C\cap D)=8\%$

From Probability Theory

$P(C\cup D)=P(C)+P(D)-P(C\cap D)\\=0.22+0.39-0.08\\P(C\cup D)=0.53$

The probability that a person owns a cat or a dog therefore is 0.53.