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
`(1)/(3).`

Step-by-step explanation: Given that
`(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.

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)=(1)/(2),~~~n(B)=(1)/(3),~~~n(A\cap B)=(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)=(P(B\cap A))/(P(A))=((1)/(6))/((1)/(2))=(1)/(3).`

Thus, the fraction of the children who have a dog also have a cat is
`(1)/(3).`