Answered

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

Verified Answer :

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.

JeanaShupp

Answer: Fraction of the people own a dog and cat \(=\dfrac{3}{50}\)

Number of people own a dog but not cat = 45

Step-by-step explanation:

Let Event A = People own a dog.

Event B= People own a cat.

Given : \(P(A)=\dfrac{9}{25}\)

\(P(B|A)=\dfrac{1}{6}\)

By using the conditional probability formula ,

\(P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\ \dfrac{1}{6}=\dfrac{P(A\cap B)}{\dfrac{9}{25}}\\\\\Rightarrow\ P(A\cap B)=\dfrac{1}{6}\times\dfrac{9}{25}=\dfrac{3}{50}\)

∴ Fraction of the people own a dog and cat \(=\dfrac{3}{50}\)

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

\(=\dfrac{9}{25}-\dfrac{3}{50}=\dfrac{2(9)-3}{50}=\dfrac{15}{50}\\\\=\dfrac{3}{10}\)

⇒ Number of people own a dog but not cat = \(\dfrac{3}{10}\times150=45\)

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