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In a certain community, 20% of the families own a dog, and 25% of the families that own a dog also own a cat. It is also known that 29% of all the families own a cat. What is the probability that a randomly selected family owns a dog?

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umairfeb221999

Answer:

The probability that a randomly selected family owns a dog, given that it doesn't own a cat, is approximately 21.12%.

Step-by-step explanation:

Let  P(D)  be the event that a randomly selected family owns a dog.

Let  P(C)  be the event that a randomly selected family owns a cat.

Then:  probability is

P (D) = 0.20

P(C) = 0.29

P(C|D) = 0.25

So, as we know

      P(D|¬ C) = P ( D ∩ ¬ C )/ P ( ¬ C )

then,

   P(D|¬ C)  [tex]=\frac{P(D)*(1-P(C|D))}{1-P(C)}[/tex]

    [tex]=\frac{(0.20)*(1-(0.25))}{1-0.29}[/tex]

    [tex]=0.2112\\[/tex]

Then, the probability that a random selected family owns a dog is 0.2112

     [tex]=21.12\%[/tex]

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