Question

Maria and John have decided that once they live in a house, they want to have a pet. 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

Explanation:

Hello!

Maria and John want to adopt a pet. The animals available for adoption are:

7 Siamese cats

9 common cats

4 German Shepherds

2 Labrador Retrievers

6 mixed-breed dogs

Total pets available: 28

To reach the probability of each pet category you have to divide the number of observed pets for the said category by the total of pets available for adoption:

P(Siam)= 7/28= 0.25

P(Comm)= 9/28= 0.32

P(Ger)= 4/28= 0.14

P(Lab)= 2/28=0.07

P(Mix)= 6/28=0.21

a.

You need to calculate the probability that the selected pet is a cat, this situation includes the categories "Siamese" and "common cat"

P(Cat)= P(Siam) + P(Comm)= 0.25+0.32= 0.57

b.

You have a total of 16 cats out of 28 pets. If you express it in the ratio: 16:28 → using 4 as a common denominator the odds of selecting a cat is: 4:7

c.

P(Cat∪Mix)

The events "cat" and "mixed-breed dog" are mutually exclusive, so you can calculate the probability of the union of both events as:

P(Cat∪Mix)= P(Cat)+P(Mix)= 0.57+0.21= 0.78

d.

Now you are in the situation that they select a dog that is not a labrador, this situation includes the categories " German shepherd" and "mixed-breed"

P(NotLab)= P(Ger)+P(Mix)= 0.14 + 0.21= 0.35

I hope this helps!