Pregunta
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Alejandro wants to adopt a puppy from an animal shelter. At the shelter, he finds six puppies that he likes: a male and female puppy from each of the three breeds of boxer, collie, and Labrador. The puppies are each so cute that Alejandro cannot make up his mind, so he decides to pick the dog randomly. Find the probability that Alejandro chooses anything except a female Labrador or a male collie. The probability is \( \square \). (Type an integer or a simplified fraction.)

Ask by Campos Lowe. in the United States
Mar 03,2025

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The probability is \( \frac{2}{3} \).

Solución

There are 6 puppies in total. The two puppies that Alejandro wants to avoid are the female Labrador and the male collie. This leaves 6 - 2 = 4 puppies that he could choose. Therefore, the probability that he picks one of the remaining puppies is 4/6, which simplifies to 2/3. The probability is 2/3.

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To find the probability that Alejandro chooses anything except a female Labrador or a male collie, we start by calculating the total number of puppies. There are 6 puppies in total: 2 boxers (1 male and 1 female), 2 collies (1 male and 1 female), and 2 Labradors (1 male and 1 female). The two puppies we want to exclude from Alejandro's choices are: 1. Female Labrador 2. Male Collie This leaves us with the following puppies to choose from: - Male Boxer - Female Boxer - Female Collie - Male Labrador So, there are 4 puppies that are not excluded. Now, the total number of puppies is 6. Therefore, the probability that Alejandro chooses anything except a female Labrador or a male collie is calculated as: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3} \] Thus, the probability is \( \frac{2}{3} \).

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