Question

At a kennel, 40% of the dogs have long hair. Of the long-haired dogs, 20% are on special diets. What is the probability that a dog selected at random from this kennel is on a special diet and long-haired?

Answer 1

The probability that a dog selected at random from the kennel is both long-haired and on a special diet is 8%.

Step-by-step explanation:

To find the probability that a dog selected at random from the kennel is both long-haired and on a special diet, you first need to calculate the probability of each independent event and then multiply them together. Since 40% of the dogs have long hair, the probability (P) of selecting a long-haired dog is P(long hair) = 0.40. Given that a long-haired dog is selected, there is a 20% chance that it is on a special diet, so the probability that a long-haired dog is on a special diet is P(special diet | long hair) = 0.20. To find the joint probability of both events occurring together (a dog being long-haired and on a special diet), you multiply the probabilities of the two events: P(long hair AND special diet) = P(long hair) × P(special diet | long hair) = 0.40 × 0.20 = 0.08.

Therefore, the probability that a randomly selected dog from this kennel is both long-haired and on a special diet is 0.08 or 8%.