Question

Patty is an animal breeder that breeds three types of dogs, along with horses, and other animals. Patty breeds the following dogs Siberian Huskies, Alaskan Malamutes, and German Shepherds. All three breeds can also be crossbreed and sold to buyers interested in popular hybrids. One of her dogs could have one, two, or all three breeds in their lineage. (Note: a dog with only one breed in their lineage is considered a pure breed dog. If it has two or more breeds in its lineage it is considered a hybrid or mixed-breed.) The following information describes the different types of animal breeding conducted by Patty.

 There are 1200 animals in total at Patty’s breeding grounds. 585 of these animals are dogs. Of the remaining animals, 212 are horses.

 10 of Patty’s dogs have a lineage that contains all three dog breeds.  There are 25 Alaskan Malamute and German Shepherd hybrids. (Possibly containing Husky bloodlines)

 There are 35 Siberian Husky and German Shepherd mixes. (Possibly containing Malamute bloodlines)

 55 of the dogs are a mix between Siberian Husky and Alaskan malamute and do not contain any other bloodlines.

 104 of the dogs are pure breed Alaskan Malamute.

 208 of the dogs are pure breed German Shepherd.

a) Draw a complete Venn diagram for the above information. Clearly label the parts

b) How many animals have a Siberian Husky bloodline?

c) An animal was selected at random from Patty’s breeding grounds. What is the probability that it was a horse or an Alaskan Malamute?

d) What is the probability that a randomly selected animal is something other than a horse or dog?

e) What proportion of dog are pure-breed?

f) What is the probability that a randomly selected animal is a dog of mixed-breed?

g) Given a dog has a Siberian Husky bloodline, what is the probability that it contains German Shephard bloodlines?

Answer 1