Question

Maria and John have decided that once they live in a home, they want to have a pet. Maria prefers cats and John prefers dogs. They go to an animal shelter and find several pets that they would love to take home. There are 7 Siamese cats, 9 common cats, 4 German Shepherds, 2 Labrador Retrievers, and 6 mixed-breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one. Answer each of the following questions separately, showing all your work to reach each answer.

a. What is the probability that they select a cat?

b. What are the odds that they select a cat?

c. What is the probability that they select either a common cat or a mixed-breed dog?

d. What is the probability that they select a dog that it is not a Labrador Retriever?

Answer 1

a) Probability that they select a cat is computed here as:
= Total number of cats / Total number of pets
= (7 + 9) / (7 + 9 + 4 + 2 + 6)
= 16/28
= 4/7

Therefore 4/7 = 0.5714 is the required probability here.

b) The odds that they select a cat is computed here as:
= Probability that a cat is selected / Probability that the cat is not selected
= (4/7) / (1 - (4/7) )
= (4/7) / (3/7)
= 4/3

Therefore 4:3 are the required odds here.

c) Probability that it is either a common cat or a mixed-breed dog is computed here as:
= Number of mixed breed dog + Number of common cat / Total number of pets
= (6 + 9) / 28
= 15/28

Therefore 15/28 = 0.5357 is the required probability here.

d) Probability that they select a dog that is not a labrador retriever is computed here as:

= (Number of German Shepherds + number of mixed breed dogs ) / Total pets
= (4 + 6)/28
= 10/28
= 5/14

Therefore 5/14 = 0.3571 is the required probability here.