Question

You ask 150 people about their pets.The results show that 9/25 of the people own a dog.Of the people who own a dog,1/6 of them also own a cat.

What fraction of the people own a dog and cat?
How many people own a dog but not cat?explain

Answer 1

9/25= 0.36, or 36%. 36% of 150 people is 54 people (0.36 x 150). 1/6= 0.1666666667 or 16.6666667%. 16.6666667% of 54 people is 9 people (0.1666666667 x 54).  9/150 or 3/50 people own both and 54 people (9/25 people) own just a dog.

Answer 2

Answer: Fraction of the people own a dog and cat
`=(3)/(50)`

Number of people own a dog but not cat = 45

Explanation:

Let Event A = People own a dog.

Event B= People own a cat.

Given :
`P(A)=(9)/(25)`

`P(B|A)=(1)/(6)`

By using the conditional probability formula ,

`P(B|A)=(P(A\cap B))/(P(A))\\\\ (1)/(6)=(P(A\cap B))/((9)/(25))\\\\\Rightarrow\ P(A\cap B)=(1)/(6)*(9)/(25)=(3)/(50)`

∴ Fraction of the people own a dog and cat
`=(3)/(50)`

Fraction of the people own a dog but not cat:
`P(A)-P(A\cap B)`

`=(9)/(25)-(3)/(50)=(2(9)-3)/(50)=(15)/(50)\\\\=(3)/(10)`

⇒ Number of people own a dog but not cat =
`(3)/(10)*150=45`