Question

The Appaloosa is an American horse breed known for its distinctive spotted coat pattern. Predecessors of the Appaloosa can be traced back to horses brought to America in the early 1600s by Spanish explorers. The Nez Perce tribe in the Northwest became widely recognized for their work in developing the Appaloosa breed.
Appaloosa coat color is derived from a base color with an overlaid spotting pattern. For example, a leopard coat pattern is considered to be a mainly white body with dark spots that flow out over the entire body. All spotting patterns on an Appaloosa are caused by having at least one allele of a gene called the leopard-complex gene.
However, Appaloosas show a wide range of spotting patterns: some have spots that extend all over the body, some have spots limited to the hip area, while others appear solid colored (and have only mottled skin). This is thought to be due to the effects of a separate gene that controls patterning.

Suppose that among Appaloosas that have genotype AA and display spotting, night blindness occurs with probability 0.45; among Appaloosas that have genotype AA and do not display spotting, night blindness occurs with probability 0.08. About 9% of all Appaloosas are genotype Aa, display spotting, and have night blindness. In Appaloosas that are genotype aa and display spotting, night blindness occurs with probability 0.12; 1% of Appaloosas that are genotype aa and do not display spotting have night blindness.
Let B represent the event that an Appaloosa has night blindness.
i. Calculate the probability that a randomly selected Appaloosa is genotype AA and has night blindness.
ii. Given that an Appaloosa is genotype AA and has night blindness, what is the probability that it exhibits spotting?
iii. If an Appaloosa is spotted and known to be genotype Aa, what is the probability that it does not have night blindness?
iv. What is the probability that an Appaloosa has night blindness, if it is known to be genotype aa?

Answer 1