In many agricultural species (plants and animals) information about particular matings can provide insights into genetic recessive conditions, and certain types of “test matings” may be utilized.
The principles of inheritance can be used to determine the probability of detection for genetic carriers. This knowledge may be the only type of genetic inference when a genetic test has not been developed, or, it may be more economically feasible in some situations such as when plants can be self-fertilized.
In cattle, black coat color is completely dominant to red. Assume a black bull (named Mr. Magic) had a red grandparent. Mr. Magic was bred to five red cows, and sired five black calves out of these red cows.
What is the probability that all five calves would have been black if Mr. Magic was a carrier for red?