Mathematics: 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?

In a certain community, 20% of the families own - id205118410, kdenormandie3122

maijahmcleod61

18.01.2022

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) $=\frac{P(D)*(1-P(C|D))}{1-P(C)}$

$=\frac{(0.20)*(1-(0.25))}{1-0.29}$

$=0.2112\\$

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

$=21.12\%$

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