Question

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 basset hound, boxer, collie, and pekinese. 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 a male puppy.
the probability of choosing a male puppy is □. (type a simplified fraction.)

Explanation:

Step1: Determine the total number of puppies

There are 8 puppies in total.

Step2: Determine the number of male puppies

Since there is 1 male puppy for each of the 4 breeds, there are 4 male puppies.

Step3: Calculate the probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (choosing a male puppy) is 4 and the total number of outcomes is 8. So \(P = \frac{4}{8}\).

Step4: Simplify the fraction

Simplify \(\frac{4}{8}\) by dividing both the numerator and the denominator by 4. \(\frac{4\div4}{8\div4}=\frac{1}{2}\)

Answer:

\(\frac{1}{2}\)