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 8 Siamese cats, 12 common cats, 6 German Shepherds, 5 Labrador Retrievers, and 11 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 is the probability that they select either a common cat or a Labrador Retriever dog? C. What is the probability that if they select a dog, that it is not a mixed breed? D. What are the odds in favor of and against choosing a Siamese cat?

A. 0.47; B. 0.40; C. 0.73; D. 0.23 & 4.26

Step-by-step explanation:

Total Animals = Total Possible Outcomes = 8 + 12 + 6 + 5 + 11 = 42 Probability = No. of Possible Outcomes / No. of total outcomes Odds in favour of event = Prob (Event) / Prob (No Event); Odds in against event = Prob (No Event) / Prob (Event)

A. Probability of choosing a Cat = All no. of cats / Total no. of animals

= (8 + 12) / 42 = 20 / 42 = 0.47

B. Probability of choosing a Common Cat or a Labrador Retriever : -

No. of common cats + no. of labrador retrievers / Total Animals

= (12 + 5) / 42 = 17 / 42 = 0.40

C. Probability of selecting non 'mixed breed' dog : -

No. of animals except mix breed dogs / Total Animals

= (8 + 12 + 6 + 5) / 42 = 31 / 42 = 0.73

D. Probability of choosing Siamese cat = Siamese Cat / Total Animals = 8 / 42 = 0.19; Probability Not choosing Siamese Cat = 1 - Prob (Siamese Cat) = 1 - 0.19 = 0.81.

Odds in favour of choosing Siamese Cat : -

Prob (Siamese cat) / Prob (Not Siamese Cat) = 0.19 / 0.81 = 0.23

Odds against choosing Siamese Cat : -

Prob (Not Siamese Cat) / Siamese Cat = 0.81 / 0.19 = 4.26