If a household has at least one cat, there is a 30% probability that the household has at least one dog. Thirty percent of households have at least one cat and 33% of households have at least one dog. Given that a household has at least one dog, the probability that the same household has at least one cat is _______ .
A)0.27
B)0.17
C)0.48
D)0.06

Question

Quizplus · Accepted Answer

To find the probability that a household has at least one cat given it has at least one dog, we use Bayes' theorem. Let $C$ be the event that a household has at least one cat, and $D$ be the event that a household has at least one dog. We are given:- $P(D|C) = 0.30$, the probability a household has a dog given it has a cat.- $P(C) = 0.30$, the probability a household has a cat.- $P(D) = 0.33$, the probability a household has a dog.We want to find $P(C|D)$, the probability a household has a cat given it has a dog. Bayes' theorem gives us:$$P(C|D) = \frac{P(D|C) \cdot P(C)}{P(D)}$$Plugging in the given values:$$P(C|D) = \frac{0.30 \cdot 0.30}{0.33} = \frac{0.09}{0.33} \approx 0.27$$

If a Household Has at Least One Cat, There Is