Question

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. What's the probability that the household owns a dog or a cat?

Answer 1

The probability that a randomly selected household owns either a dog, a cat, or both is 54%, calculated by adding the probabilities of owning a dog and a cat and subtracting the intersection of both.

Step-by-step explanation:

The probability that a household owns a dog or a cat can be calculated using the formula for the probability of the union of two events, which accounts for the fact that some households may own both a dog and a cat. To find the probability of a dog or a cat (or both), we add the probability of owning a dog to the probability of owning a cat and subtract the probability of owning both, since these households have been counted twice.

P(Dog or Cat) = P(Dog) + P(Cat) - P(Dog and Cat)

P(Dog or Cat) = 40% + 32% - 18%

P(Dog or Cat) = 54%

Thus, the probability that a randomly selected household owns either a dog, a cat, or both is 54%.