Question

1/2
of the children within the city limits have a dog,
1/3
have a cat, and
1/6
have a dog and a cat. What fraction of those who have a dog also have a cat?

Answer 1

It is 1/6 because it says that in the problem that "1/6 people have a dog and a cat" and it is asking "What fraction of those who have a dog also have a cat?" It says the answer in the problem

Answer 2

Answer:  The fraction of the children who have a dog also have a cat is $\dfrac{1}{3}.$

Step-by-step explanation:  Given that $\frac{1}{2}$ of the children within the city limits have a dog,  $\frac{1}{3}$  have a cat, and  $\frac{1}{6}$  have a dog and a cat.

We are to find the fraction of those children who have a dog also have a cat.

Let, S denote the sample space of the given experiment.

Then, n(S) = 1.

Let, event A and event B represents the fractions of children having a dog and a cat respectively.

Then, according to the given information, we have

$n(A)=\dfrac{1}{2},~~~n(B)=\dfrac{1}{3},~~~n(A\cap B)=\dfrac{1}{6}.$

The fraction of children who have a dog also have a cat is given by the conditional probability of event B given A.

That is, he required probability is

$P(B/A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{\frac{1}{6}}{\frac{1}{2}}=\dfrac{1}{3}.$

Thus, the fraction of the children who have a dog also have a cat is $\dfrac{1}{3}.$