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A man wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he likes, a male and female puppy from each of the four breeds of water spaniel, bullmastiff, dachshund, and Labrador. The puppies are each so cute that he cannot make up his mind, so he decides to pick the dog randomly. Find the probability that the man chooses anything but a Labrador. The probability is \( \square \). (Type a simplified fraction.)

Ask by Hardy Watson. in the United States
Mar 03,2025

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Answer

The probability is \( \frac{3}{4} \).

Solution

There are 8 puppies in total, and 2 of them are Labradors (one male and one female). So, the number of puppies that are not Labradors is 8 - 2 = 6. Therefore, the probability that he chooses a puppy that is not a Labrador is 6/8, which simplifies to 3/4. The answer is 3/4.

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To find the probability that the man chooses anything but a Labrador, we first identify the total number of puppies and the number of Labrador puppies available. There are eight puppies in total: two from each of the four breeds. The breeds are water spaniels, bullmastiffs, dachshunds, and Labradors. Since there are two Labradors, the total number of puppies that are not Labradors is: Total puppies - Labrador puppies = 8 - 2 = 6. Now, the probability of picking a puppy that is not a Labrador is the number of non-Labrador puppies divided by the total number of puppies: Probability = Number of non-Labrador puppies / Total number of puppies = 6 / 8. This fraction can be simplified: 6 / 8 = 3 / 4. Therefore, the probability that the man chooses anything but a Labrador is \( \frac{3}{4} \).

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