In a certain community, 25% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also know that 28% of all the families own a cat. What is the probability that a randomly selected family owns a cat?
What is the conditional probability that a randomly selected family owns a dog given that it doesn't own a cat?
What is the conditional probability that a randomly selected family owns a dog given that it doesn't own a cat?
1 Answer
The probability that a randomly selected family owns a cat is 28%.
The conditional probability that a randomly selected family owns a dog, given that it doesn't own a cat, is approximately 27.8%.
Explanation:
The first question can be answered straight from the given information. If 28% of all the families own a cat, then the probability of randomly selecting a family that owns a cat is 28%.
Let
Let
Then:
We want to find: