In one large city. 40% of all households own a dog. 32% own a cat, and 18% own both. Suppose we randomly select a household and learn that the houschold owns a cat. Find the probability that the household owns a dog. P(Dvert C)=0.18 P(Dvert C)=0.54 P(Dvert C)=0.563 P(Dvert C)=0.40

Let D be the event that a household owns a dog, and C be the event that a household owns a cat. We are given the following probabilities:<br /><br />* P(D) = 0.40 (Probability of owning a dog)<br />* P(C) = 0.32 (Probability of owning a cat)<br />* P(D ∩ C) = 0.18 (Probability of owning both a dog and a cat)<br /><br />We are asked to find the probability that a household owns a dog given that it owns a cat, which is written as P(D|C). We can use the formula for conditional probability:<br /><br />P(D|C) = P(D ∩ C) / P(C)<br /><br />Plugging in the given values:<br /><br />P(D|C) = 0.18 / 0.32<br />P(D|C) = 0.5625<br /><br />Rounding to three decimal places, we get 0.563.<br /><br />Therefore, the probability that the household owns a dog given that it owns a cat is 0.563. So the correct answer is $P(D\vert C)=0.563$.<br />Final Answer: The final answer is $\boxed{0.563}$<br />