Question

In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is the conditional probability that a randomly selected family owns a dog given that it owns a cat?

Answer 1

To find the conditional probability that a randomly selected family owns a dog given that it owns a cat, we can use the formula for conditional probability. Given the percentages of families owning a dog and a cat, we can calculate the conditional probability using the formula.

Step-by-step explanation:

To find the conditional probability that a randomly selected family owns a dog given that it owns a cat, we can use the formula for conditional probability: P(A|B) = P(A and B) / P(B).

Given that 36 percent of the families own a dog (P(A)) and 22 percent of the families that own a dog also own a cat (P(B|A)), we can calculate:

P(A and B) = P(A) * P(B|A) = 0.36 * 0.22 = 0.0792.

Additionally, we know that 30 percent of the families own a cat (P(B)), so:

P(B) = 0.30.

Now we can substitute these values into the formula:

P(A|B) = P(A and B) / P(B) = 0.0792 / 0.30 ≈ 0.264 or approximately 26.4%.